Shofar, Sukkah, vLulav - Chapter Five

In contrast to the walls mentioned in the last halachah of the previous chapter...

[There are requirements regarding] the s'chach of a sukkah, and not all substances are acceptable [to be used for this purpose]. - Some of the requirements mentioned by the Rambam were established by Torah law, while others are Rabbinic ordinances, as explained below.

For s'chach, we may use only a substance which:

a) grows from the ground - i.e., is an agricultural product and is neither found naturally - e.g., metals - nor produced from animals nor manufactured synthetically;

b) has been detached from the ground - and is not still connected to its source of nurture;

c) is not subject to contracting ritual impurity - This excludes articles used as food and those that have been fashioned into utensils. These three requirements are alluded to by Deuteronomy 16:13: "Make the Sukkot holiday for yourselves for seven days, when you gather in from your grain and grapes..."

Sukkah 12a explains that the verse implies that the s'chach, the essential element of the sukkah, must resemble "the leftovers from the grain and grape harvest."

(The expression "alluded to" was used rather than "derived from" on the basis of the Rambam's commentary on the Mishnah, Sukkah 1:4. That expression implies that the concept cannot be derived from the verse per se. Rather, it was transmitted as a halachah l'Moshe miSinai, and the Biblical verse is merely an allusion.)

The Rambam gives examples of entities which are not acceptable as s'chach on the basis of these principles in the following halachah.

d) does not have an unpleasant odor - As implied by the following halachah, this and the following clause are Rabbinic decrees. S'chach with an unpleasant odor will not create an inviting holiday environment. Indeed, substances with an unpleasant odor should not be used for the sukkah's walls either.

e) and does not have elements which fall off and wither constantly - for a person will not be pleased to have portions of the s'chach falling into his food. The Mishnah Berurah 629:39 states that the prohibition applies to elements that fall off naturally. However, if they fall off only when subjected to wind, there is no difficulty in using them.

When a person uses as s'chach a substance which does not grow from the ground, is still connected to the ground, or is subject to contracting ritual impurity, [the sukkah] is not acceptable. - for these requirements stem from the Torah itself. The particular aspects of these requirements are described in this and the following halachot.

However, if he transgressed and used as s'chach a substance which has elements which fall off and wither - Sukkah 13a gives the shrub known as hollow as an example of such a substance.

or possesses an unpleasant odor - Sukkah 12b gives the plant known as wormwood as an example of such a substance.

it is kosher - after the fact, for these are only Rabbinic requirements. The Mishnah Berurah 629:38 emphasizes that even if other s'chach is available, there is no need to remove the s'chach with the unpleasant odor. However, the Pri Megadim stresses that if the odor is so unpleasant that no one would bear it in his home, it is forbidden to use such a sukkah.

[Our Sages] - Sukkah 13a

said only that one should not use these as s'chach lest one leave one's sukkah and depart.

One must take care that the branches and leaves should not descend within ten handbreadths of the ground - the minimum height for a sukkah prescribed in Chapter 3, Halachah 1.

so that one will not be uncomfortable - Sukkah 4a describes this as "a disgusting dwelling, unfit for human habitation."

when using the sukkah. - The Rambam's phraseology leaves room for the interpretation that this is a suggestion, but not an absolute requirement. (See Rabbenu Manoach.) Nevertheless, the Shulchan Aruch (Orach Chayim 633:9) states that such a sukkah is unacceptable for use.

If one used metals - even if they have not been made into utensils, but are still in a raw state in which they are unfit to contract ritual impurity;

bones, or hides - even if they have not been made into garments, but are still in a raw state in which they are unfit to contract ritual impurity;

as s'chach, it is unacceptable, because these do not grow from the ground.

If one suspended vines and the like over it until they made a sukkah, it is unacceptable, because they were not uprooted [from the ground]. - The laws governing the use of such plants as s'chach after they have been hung over the sukkah and then detached from the ground are discussed in Halachah 12.

Should one use wooden utensils - In particular, this refers to wooden utensils that have a receptacle or are wide and other articles are frequently placed upon them - e.g., a table. However, wooden utensils that do not fall into these categories are not subject to contracting ritual impurity, and, hence, may be used for s'chach. An example of such utensil is a ladder. The Rambam (Hilchot Keilim 4:1) declares that a ladder is not subject to contracting ritual impurity. Hence, according to his opinion, there is no difficulty with using it as s'chach.

(It must be emphasized that other authorities question the Rambam's decision on a ladder and maintain that a ladder may be subject to contracting ritual impurity. Hence, it is preferable not to use it as s'chach. See the Shulchan Aruch and Ramah, Orach Chayim 629:7.)

mats that were made to lie on - However, mats that were made for use as s'chach or for shade may be used as s'chach. Halachah 6 discusses the laws which apply when a mat was made without any specific intention.

and the like as s'chach, it is unacceptable, because they are subject to contracting ritual impurity. Similarly, using broken - e.g., utensils with holes of sufficient size to render them no longer subject to contracting ritual impurity. (See Hilchot Keilim, Chapter 6.)

and worn out - e.g., garments that have worn out and are less than three fingerbreadths by three fingerbreadths in size and, hence, are no longer subject to contracting ritual impurity (Sukkah 16a; Hilchot Keilim 22:21).

utensils as s'chach is unacceptable. - This is a Rabbinic decree on the basis of the following rationale...

Since these substances were subject to ritual impurity - previously,

[the latter law was instituted] lest one use broken pieces - from utensils

which have not yet attained a state of [unquestionable] purity - i.e., are still subject to contracting ritual impurity.

as s'chach.

If one used foods - This refers only to foods for humans. Food which is eaten primarily by animals is not subject to contracting ritual impurity (Hilchot Tum'at Ochlin 1:1) and hence may be used as s'chach (Taz 629:12).

as s'chach, it is unacceptable, because they are subject to contracting ritual impurity. - There is a slight imprecision in the Rambam's statements. Produce is not subject to contracting ritual impurity until it comes into contact with liquid. (See Leviticus 11:38; Hilchot Tum'at Ochlin 1:1-2.) Nevertheless, foods are not fit to be used as s'chach even though they have never come into contact with water (Shulchan Aruch HaRav 629:1; Mishnah Berurah 629:28).

[When one uses] branches from a fig tree which contain figs, runners from a grape vine which contain grapes, branches of a date palm which contain dates and the like - i.e., the difficulty being that although the branches are proper s'chach, the fruit is unfit to be used for that purpose...

[the following rules apply:] We see if the waste - the branches and leaves

is more than the food - the fruit

then we may use them as s'chach. If not, we may not use them as s'chach. - Rabbenu Manoach explains that these decisions are based on the principle that according to Torah law, mixtures are categorized according to the majority (בטל ברב).

On the basis of Sukkah 13b-14a, the Shulchan Aruch (Orach Chayim 629:10) explains that sometimes the stems of the fruit are considered part of the fruit, and on other occasions part of the branches. The Magen Avraham 629:12 explains that generally, a stem is not considered to be longer than three handbreadths. However, there are certain instances (e.g., grains) when a longer measure is considered. Hence, it is proper to be stringent in this regard. (See also Shulchan Aruch HaRav 629:15-16.)

The apparent contradiction between this halachah and Halachah 13 is discussed in the commentary on that halachah.

If one uses as s'chach vegetables - The Maggid Mishneh explains that this refers to vegetables that are used as animal food, and hence were not excluded by the previous clause of this halachah. Rabbenu Manoach and the Shulchan Aruch (Orach Chayim 629:12) explain that this refers to vegetables that are eaten by humans. Sukkah 13b appears to support the latter interpretation, stating:

The vegetables with which a person can fulfill his obligation on Pesach... [can] invalidate a sukkah, [because they are considered] to be vacant space.

which, when they dry up, will wither, and none of their substance will remain - i.e., the vegetables will dry up and wither during the Sukkot festival, leaving the sukkah with more vacant space than shade (Kessef Mishneh).

even though they are now fresh, their place is considered to be vacant, as if they did not exist. - According to the Maggid Mishneh's interpretation, the explanation of the law is straightforward. It teaches us that rather than consider the vegetables to be non-kosher s'chach, we consider their space to be vacant. The latter interpretation requires a slightly more intricate explanation. The vegetables are not considered to be non-kosher s'chach, which would invalidate the sukkah if they take up four handbreadths, as explained in Halachah 14. Rather, their space is considered to be empty. Hence, a space of three handbreadths is sufficient to invalidate the sukkah, as explained in Halachah 20.

If one used as s'chach branches of flax which were not crushed and combed, they are kosher, because they are still considered to be wood. - The use of the word עץ, rendered as branches or wood, with regard to flax, has its source in Joshua 2:6, which describes how Rachav "hid them in branches of flax."

After the flax has been crushed and combed - The Rishon Letzion questions the law when the flax has been crushed but not combed, and concludes that as long as it has not been combed, it is acceptable. Nevertheless, Shulchan Aruch HaRav 629:5 does not accept this conclusion.

it may not be used as s'chach - Though it is not considered to be a garment and, hence, is not subject to contracting ritual impurity (Maggid Mishneh; see also Shabbat 27b), it may nevertheless not be used as s'chach...

since its form has changed and it is as though it is no longer a product of the earth. - The Ra'avad disagrees with this principle and states that even before it is woven into a garment, flax is useful to stuff pillows and covers. Hence, it is subject to contracting ritual impurity and is thus unfit to be used as s'chach.

The Maggid Mishneh points out a contradiction to the Ra'avad's logic. The "male arrows" mentioned in the following halachah are - like flax - prepared to be used for a purpose. Nevertheless, they are considered acceptable for use as s'chach.

Rav Kapach mentions two possible extensions of the difference of opinion between the Rambam and the Ra'avad:

a) paper or carton - According to the Rambam, it may not be used because it no longer resembles a plant produced from the earth. According to the Ra'avad, it might be acceptable, since it is not subject to contracting ritual impurity.

b) cotton wool - It may be used for the purposes mentioned by the Ra'avad and thus, according to his opinion, would be subject to contracting ritual impurity. Nevertheless, its natural form is preserved. Hence, according to the Rambam's opinion, it would be acceptable. (It must be noted that the Magen Avraham 629:3 and Shulchan Aruch HaRav 629:5 maintain that after cotton has been combed, it is considered as though its form has been altered.)

One may use ropes made from palm bast or hemp and the like as s'chach, since their original form is unchanged and ropes are not considered to be utensils. - nor are they subject to contracting ritual impurity. The Shulchan Aruch, Orach Chayim 629:5 quotes this law as halachah, but adds that ropes of flax and canvas may not be used for this purpose.

[The following rules apply] when one uses arrows as s'chach. - The question whether the arrows are acceptable as s'chach or not revolves around another issue - their susceptibility to contracting ritual impurity.

Those which are "male" - i.e., the end of their body is sharpened and comes to a point, which is intended to be put inside a metal arrowhead.

are kosher - for the arrow itself is considered a simple wooden utensil which is not susceptible to contracting ritual impurity. (See Hilchot Keilim 1:10.)

The Magen Avraham 629:2 states that this decision applies only before these arrows were placed in the arrowhead. If they have been placed in the arrowhead, even if subsequently removed they are no longer acceptable as s'chach.

those which are "female" - i.e., the end of their body is hollowed out for the arrowhead to be inserted within

are not acceptable. - for they are subject to contracting ritual impurity.

Even though [ultimately,] they will be filled with iron - Hilchot Keilim 2:3 states: "A receptacle which is made to be filled is not considered a receptacle." Thus, one might assume that these arrows would also not be considered as having a receptacle. The Pri Ha'aretz explains that since the iron arrowheads are often removed from these bodies, it is considered as though...

they have a receptacle. Hence, they are susceptible to contracting ritual impurity, as are all utensils with receptacles. - It must be noted that Rashi and other commentators follow the simple interpretation of Sukkah 12b (the source for this law) and disagree with the Rambam's decision in Hilchot Keilim. They maintain that if a utensil has a receptacle, even if it will be permanently filled, it is subject to contracting ritual impurity.

A mat of reeds, of raw rubber, or of hemp - if it is small, we may assume that it was made to lie on. - The commentaries note an apparent contradiction in the Rambam's words. Hilchot Keilim 25:13 states that even a small mat of reeds or hemp is not subject to contracting ritual impurity, because it is uncomfortable to lie on.

Therefore, it may not be used for s'chach unless it was [explicitly] made for this purpose. - Since the mat was made with that specific intention, we do not follow the general principles, but rather judge it individually.

If it is large - The Rambam's statements are based on Sukkah 20a. It must be noted that his decisions are dependent on the version of the text of the Talmud he accepted. The Ra'avad and others interpret the word גדולה as related to the word גדיל (tassel). Thus, they explain that the Talmud is referring to a small mat. However, because it is made of thick tassels, rather than woven, it is not comfortable to lie on, and hence would most likely be used for shade. According to this opinion, any woven mat, even if it is large, is unfit to be used as s'chach. The Shulchan Aruch (Orach Chayim 629:6) quotes the Rambam's interpretation.

we may assume that it was made for shade; therefore, it may be used for s'chach unless it was [explicitly] made to lie on. - The Ramah (Orach Chayim, ibid.) mentions that in places where it is customary to affix mats permanently as the roofs for homes, they may not be used for s'chach. The Rabbis instituted this decree lest people remain in their homes on Sukkot without differentiating between them and a sukkah.

If it has a border - a small lip (Sukkah 20b)

even a large mat may not be used as s'chach, because it is considered to be a receptacle. - Tosafot, Sukkah 20b quotes Ketubot 50b, which explains that such mats were used to collect dates.

Even if the border was removed, it may not be used as s'chach, because it would be considered to be a broken utensil. - which, as explained in Halachah 2, may not be used as s'chach even though they are not susceptible to contracting ritual impurity.

Boards which are less than four handbreadths wide - In many places throughout the Talmud, four handbreadths is established as the minimum size of an area. Hence, a board of that size is considered significant and may not be used as s'chach (Sukkah 14a).

may be used for s'chach even though they have been planed - smooth, and thus are fit to be used in their present state (Sukkah 15a; Rabbenu Manoach).

If they are more than four handbreadths wide, they should not be used as s'chach, even though they have not been planed. This is a decree [instituted] lest one sit under a roof and regard it as a sukkah. - A person might think: "What is the difference between the sukkah and my house - they are both covered with boards?" This is surely a false assumption. As explained in the following halachah, since the boards of a roof were not placed there for the purpose of shade, but rather to be part of the permanent structure of the house, they cannot be considered to be s'chach (Sukkah 14a; Rabbenu Manoach).

If one placed a board which was more than four handbreadths wide over [a sukkah, the sukkah] is kosher. - The Maggid Mishneh explains that this applies only when the board is placed at the side of the sukkah. Thus, it could be considered to be an extension of the wall (דופן עקומה), as explained in Halachah 14. However, if it is in the midst of the sukkah, it is not acceptable. The Kessef Mishneh explains that this law can apply even in the midst of a sukkah, provided the sukkah already possesses its minimum size. His decisions in the Shulchan Aruch, Orach Chayim 632:1 follow this interpretation.

However, one should not sleep under the board. - According to the Maggid Mishneh, because it is part of the wall; according to the Kessef Mishneh, because it appears to be a separate domain.

A person who did sleep - or fulfilled any other of the activities which must be performed in the sukkah

under the board has not fulfilled his obligation.

There were boards that were four handbreadths wide, but less than four handbreadths thick. A person turned them on their side so that they would not be four handbreadths wide to use them as s'chach. This is not acceptable, because a board is unacceptable for use as s'chach whether one uses its width or thickness. - Sukkah 14b explains that after the Sages forbade the use of such boards, they are considered to be equivalent to iron poles.

The Magen Avraham 629:22 writes that at present it is customary not to use boards as s'chach, even if they are less than four handbreadths wide. However, if there is no other s'chach available, one may use boards for that purpose even if they are more than four handbreadths wide.

A roof which is not covered by a ceiling - i.e., the plaster and the stones - but rather has only boards fixed in place, is not acceptable, since they were not placed there for the purpose of a sukkah - as required by the following halachah

but to be part of the house. Therefore, if one - performed two activities:

a) lifted up the boards - from their place. (Though the Shulchan Aruch, Orach Chayim 631:9 does not mention this requirement, the Mishnah Berurah 631:4 does.)

and b) removed the nails - holding the boards in position. (See the Rambam's commentary on the Mishnah, Sukkah 1:7.) Through these actions, one is considered to have nullified the previous placement of the boards, and it is considered as though they have been placed there...

with the intent [that they serve] as a sukkah - Therefore

it is kosher - for the boards are essentially fit to be used as s'chach. The only difficulty was the intention with which they were originally placed. A change of mind without an act is not sufficient, since, as explained in the commentary on the following halachah, we are required to "make" a sukkah and not use one which has already been made.

[This applies provided] that each board is not four handbreadths wide. - as explained in the previous halachah. Rabbenu Asher states that in such a situation, the sukkah is acceptable even though the boards are more than four handbreadths wide.

He explains that in the previous instance, the reason the Sages forbade using such boards was to differentiate between them and the boards of a house. In the present instance, the fact that the person took apart the roof of his house obviously implies that he realizes that it may not be used as a sukkah. Hence, there is no need for such a decree. This opinion is accepted by the Shulchan Aruch, ibid.

A sukkah that was made for any purpose whatsoever - even if it was not made for the purpose of [fulfilling] the mitzvah - if it was made according to law - Sukkah 8b quotes a baraita which contains the latter statement and questions: "What does 'according to law' mean?...That it was made for the purpose of shade."

It appears that the Rambam uses the same expression, but with different implications. Since he explicitly states that the sukkah must be constructed for the purpose of shade, one might infer that the expression "according to law" is intended to include other concepts. Thus, it can be a reference to the requirements for a sukkah's size and the nature of the materials used for the s'chach, as mentioned in this and the previous chapter.

it is kosher. - The Mishnah, Sukkah 1:1, states:

An old sukkah: The School of Shammai deems it unacceptable, while the School of Hillel rules it kosher.

The commentaries explain that the term "an old sukkah" refers to any sukkah that was constructed for purposes other than the fulfillment of the mitzvah.

In its discussion of this law, the Jerusalem Talmud requires that one must make an addition or change to the s'chach. Though that decision is not quoted by the Rambam, Rabbenu Asher mentions it and it is accepted by the Shulchan Aruch (Orach Chayim 636:1). Nevertheless, the Magen Avraham 636:1 explains that this is a desirable and proper step, but the sukkah is acceptable even though no changes have been made.

However, it must be made for the purpose of shade. - Isaiah 4:6 states: "It shall be a sukkah for shade from the heat...," thus defining the purpose of such a structure. A sukkah constructed for the purposes of modesty is not acceptable (Rabbenu Manoach).

Examples of this are sukkot made for gentiles, sukkot made for animals, and the like - which are outside the entire framework of mitzvot. Sukkah 8b also mentions the sukkot made for shepherds and watchmen. Though the latter are obligated to keep the mitzvah of sukkah, they did not necessarily construct their sukkot with that intent in mind.

In contrast, a sukkah that came about on its own accord - e.g., branches fell over a frame, and of course, any time a roof is covered for other purposes - e.g., the construction of a home, as mentioned in the previous halachah...

is unacceptable, because it was not made for the purpose of shade.

Similarly, when a person hollows out a place in a heap of produce and thus makes a sukkah, it is not considered to be a sukkah - Sukkot 12a explains that there is an added factor involved in this example. Deuteronomy 16:13 states: "Make a [celebration of] the Sukkot holiday for seven days." This refers to the construction of the sukkah and teaches that we must "make" a sukkah and not use what was already made. Therefore, despite the fact that the person hollowed out the space for the purpose of shade, the sukkah is not acceptable, because the produce was not originally placed there for that purpose.

We find a similar principle concerning tzitzit. Deuteronomy 22:12 states: "Make yourself tassels on the four corners of your garments." On the basis of this command, Menachot 40b teaches that it is unacceptable to tie tzitzit to a three-cornered garment and then cut a fourth corner, since we are required to make tzitzit, and not use what is already made.

for the produce was not piled there for this purpose. - The Ba'al Hamaor writes that if, originally, a person were to pile produce with the intention that later he would hollow out a sukkah, the sukkah would be acceptable. However, this opinion is not accepted by other authorities.

Accordingly, were one to create a space one handbreadth [high] - We find the measure of one handbreadth considered to define a structure with regard to the laws of ritual impurity. Accordingly, it is given significance in this context as well. (See Sukkah 16a.)

and seven [handbreadths] - by seven handbreadths

in area for the purpose of a sukkah, and afterwards hollow it out till it reached ten [handbreadths] - the minimum height of a sukkah, as explained in Chapter 3, Halachah 1.

it is kosher, since its s'chach was placed for the purpose of shade - and then, the original structure was merely expanded.

We may not use bundles of straw, bundles of wood or bundles of reeds as s'chach. - Although, according to the Torah's requirements, these would be considered proper s'chach...

This decree [was instituted] - by the Sages (Sukkah 12a)...

lest one place those bundles on one's roof to dry out, and then change one's mind and sit under them with the intent [that they serve as] a sukkah. The person did not place the s'chach there originally for the purpose of shade. Thus, it resembles a sukkah that came about on its own accord. - which is unacceptable, as explained in the previous halachah.

If one - placed bundles of these substances on a roof with the intent that they would be used as s'chach and...

untied [the bundles], they are acceptable [for use as s'chach]. - The Shulchan Aruch (Orach Chayim 629:17) explains that a different rule applies if the bundles were originally placed on the roof to dry out. For them to be acceptable as s'chach, untying them alone is insufficient, and one must also shift the position of their contents.

A bundle is considered to be no fewer than twenty five units. - Thus, any lesser amount of these substances are acceptable as s'chach even though they are tied together.

The Rambam bases his statements on the Jerusalem Talmud (Sukkah 1:6). Though the Ra'avad maintains that a bundle may be composed of even a smaller number of units, the Rambam's opinion is accepted as halachah by the Shulchan Aruch (Orach Chayim 629:15.

Though the Sages instituted the decree mentioned in the previous halachah, they made certain exceptions. Therefore...

Small bundles - The Kessef Mishneh questions the reason for the addition of the adjective, noting that if the bundles contain fewer than twenty five units, they are permitted, as stated in the previous halachah. Others mention that this refers to bundles of small branches.

that were tied together [to be sold] by number - to be untied immediately thereafter (Shulchan Aruch, Orach Chayim 629:16).

may be used as s'chach. - Sukkah 13b relates that bundles of this nature were frequently used in Sura, and that the Sages permitted them to be used as s'chach.

Similarly, if one cuts off the top of a date palm and the branches are bound to it, it may be used as s'chach, because elements that are bound naturally are not considered to be bundles. - The Ba'al Hamaor questions whether this principle applies only with regard to s'chach, where it is logical to assume that a more lenient position would be taken, since the entire question revolves around a Rabbinic decree, or whether it also applies in all cases where Torah law itself requires a bundle.

Furthermore, even if one tied the tops of the branches from one side and they thus appear to be a single bundle with one of its two ends bound naturally and the other bound as a result of human activity, it may be used as s'chach. A tree which is bound up is not considered to be a bundle, but rather a single piece of wood, since [the branches] are bound together naturally. - However, if one were to add even one branch and then tie them together, it would be considered to be a bundle (Shulchan Aruch, Orach Chayim 629:15).

Similarly, any knot which is not strong enough to hold when carried is not considered a knot [and the resulting bundle may be used as s'chach]. - Sukkah 13b mentions this principle when explaining why bundles of willows whose upper tie was loosened could be used as s'chach.

A person who constructs his sukkah under a tree is considered as though he built it within his home - and the sukkah is unacceptable. This applies only when the shade the tree produces exceeds the open area. However, if there is more open space under the tree than shade, the sukkah may be kosher.

The determination of whether such a sukkah is kosher depends on a number of principles, based on the interpretation of Sukkah 9b and 11a. The Rambam's interpretation of that passage, and thus the ground rules he establishes, differ from those accepted by the Shulchan Aruch (Orach Chayim 626:1-2).

In the following halachah, the Rambam deals with the resolution of the question when no effort has been made to correct the problem of the non-kosher s'chach. As will be explained, there his interpretation is contested by other authorities. In this halachah, the Rambam describes the rulings which govern the situation when an effort has been made to rectify the situation by detaching the branches from their source of nurture. These are based on the Mishnah, Sukkah 11a, and are also accepted by other Rabbinic authorities. (See the Shulchan Aruch, Orach Chayim 626:2.)

If one draped the leaves and branches of trees [over the sukkah], and then placed s'chach over them, and only afterwards detached them - As mentioned in Halachot 1 and 2, branches are fit to be used for s'chach only after they have been detached from their source of nurture.

[the following rules apply:]

If the amount of [kosher] s'chach exceeded [the branches], it is kosher. - Though at present, the branches would be acceptable as s'chach, as explained in the commentary on Halachah 9, the Torah requires that when s'chach is originally put in place, it must be kosher. Otherwise, it is unacceptable even though steps were taken to correct the disqualifying factors. This is based on the principle that one must make a sukkah and not use one which is already made.

Nevertheless, since the prohibition against using these branches as s'chach does not relate to their essential nature, their presence may be nullified when there is a majority of kosher s'chach. This conforms to the principle of ביטול ברב.

If the amount of s'chach which originally was kosher did not exceed [the branches] - the presence of the branches remains halachically significant. Hence,...

one must move them - i.e., each of the branches individually (Shulchan Aruch, ibid.)

after detaching them, so that they will have been put in place for the purpose of a sukkah. - Moving the branches negates their previous placement, and afterwards they are considered to be kosher s'chach, which was put in place for the purpose of creating a sukkah.

If one mixed a substance which may be used for s'chach with a substance that may not be used for s'chach - This may refer to a substance like metal, which is unfit for use as s'chach because it does not grow in the earth, or branches of a tree which have not been detached from their source of nurture.

and used - the mixture of...

the two as s'chach, even though the quantity of kosher s'chach exceeds that of the substance which was not acceptable as s'chach - The presence of the substance which is not acceptable as s'chach is not nullified according to the principles of ברב ביטול, because it exists as a separate entity which can be distinguished from the kosher s'chach.

Rav Avraham, the Rambam's son, notes the apparent contradiction between this decision and Halachah 3, which states:

[When one uses] branches from a fig tree which contain figs,...We see if the waste is more than the food; then we may use them as s'chach.

That halachah also mentions kosher s'chach - the branches - and substances which are not acceptable as s'chach - the figs. However, if there is a greater quantity of branches, the presence of the figs is nullified. In contrast, in this halachah, that concept is not applied.

Rav Avraham distinguishes between the two. In Halachah 3, the person does not intend to use the fruit for the purpose of shade; he merely wants to save the effort of removing it from the branches. Therefore, their presence may be nullified. In contrast, in this halachah the substances which are not acceptable as s'chach are being employed for the purpose of shade itself. Hence, their presence cannot be nullified.

[the mixture] is not acceptable. - As mentioned above, this decision depends on the Rambam's interpretation of Sukkah 9b. That passage reads:

A person who constructs his sukkah under a tree is considered as though he built it within his home...

Ravva said: "The above applies only to a tree whose shade is greater than its open space. However, if its open space is greater than its shade, it is kosher.

What difference does it make if its open space is greater than its shade, the substance not acceptable as s'chach will be combined with the kosher s'chach [and therefore, the sukkah will not be acceptable]?

Rav Pappa said: בשחבטן.

The Maggid Mishneh, the Ra'avad, and Rabbenu Manoach explain that the Rambam renders בשחבטן as "when he separated them." Thus, when the two substances were combined, the Rambam's opinion would be that the sukkah is not kosher, as explained in this clause of the halachah. When they are separate, the sukkah may be kosher according to the stipulations mentioned in the following clause of this halachah and the halachot to come.

(The Kessef Mishneh explains that the Rambam renders בשחבטן as "when he severed them." However, that difference in interpretation does not result in a difference in halachah.)

Rashi and others interpret בשחבטן as "when he lowered them (and mixed them together with the kosher s'chach)." Thus, according to this opinion, the sukkah is acceptable when the kosher and non-kosher s'chach are mixed together. Thus, this view is diametrically opposed to the Rambam's, who maintains that such a mixture is of no avail.

As noted by the Shulchan Aruch (Orach Chayim 626:1), there are two ways of understanding this interpretation of the passage. However, since both of them are not acceptable to the Rambam, their explanation will not be included here.

If one covered the sukkah with the two substances and kept them separate - When there is a majority of kosher s'chach, it is judged to be an independent entity. When there is a sufficient amount of kosher s'chach, the sukkah is kosher unless the substance that is not acceptable as s'chach is placed in a manner which can disqualify the entire sukkah, as is explained in this and the following three halachot.

[the following rules apply:] If there are more than three handbreadths of the substance which is not acceptable as s'chach in one place - The principle of l'vud, by which this substance could be considered to be a continuation of the kosher s'chach, cannot apply. However, if there is less than three handbreadths of the substance that is not acceptable as s'chach in one place, even though there are a number of such patches among the s'chach, the sukkah is kosher, as stated in Halachah 16. Furthermore, one may eat and sleep under the non-kosher s'chach (Shulchan Aruch, Orach Chayim 632:1).

whether - the substance which is not acceptable as s'chach is placed...

in the middle of the sukkah or at its side, it is not acceptable. - As stated in the following halachot, this is relevant only with regard to a sukkah which possesses the minimum area. The reason the sukkah is not acceptable is not that it is disqualified by the non-kosher s'chach, but that it does not have the minimum amount of kosher s'chach (Sukkah 17b).

Where does the above apply? In a small sukkah. - See the commentary on both the previous and following halachot.

However, in a large sukkah - which possesses a minimal amount of kosher s'chach, more lenient rules apply...

where there is a substance that is unacceptable as s'chach in the middle, it disqualifies the sukkah if there are four handbreadths of it - across the entire span of the sukkah, dividing the sukkah in half, it is considered to be significant (Rashi, Sukkah 17a), and hence the sukkah is disqualified.

The Ramah (Shulchan Aruch, Orach Chayim 632:2) emphasizes that even where the non-kosher s'chach is of this size, if the sukkah possesses seven cubits by seven cubits of kosher s'chach in one place, that portion may be considered to be a kosher sukkah and used during the holiday.

[If there is] less than that - the division is not as noticeable. Hence,

the sukkah is kosher. - The Shulchan Aruch (Orach Chayim 632:1) states that one may eat and sleep throughout the entire sukkah. However, the Ra'avad and Rabbenu Nissim do not accept this leniency, and the Mishnah Berurah (632:3) advises following this stringency.

Where the substance that is unacceptable as s'chach is at the side, it disqualifies the sukkah if there are four cubits of it. - Four cubits or more exceeds the measure of leniency provided by the Torah.

[If there is] less than that, the sukkah is kosher. - on the basis of the principle of דופן עקומה explained below.

For example, a) [the roof of] a house which was opened in the center and s'chach placed over the opening - This and the following examples are given by the Mishnah, Sukkah 1:10.

b) a courtyard surrounded by an excedrah - note the drawing accompanying Chapter 4, Halachah 8.

which was covered with s'chach - Sukkah 17a explains that one might not necessarily have been able to deduce this example from the previous one, because in that instance the walls of the house were constructed for it. In contrast, the walls of the excedrah were not constructed for its sake, but for the houses on either side.

c) a large sukkah over which was placed a substance that was not acceptable as s'chach near the sides of its walls. - Sukkah 17a explains that one might not necessarily have been able to deduce this example from the previous ones, because in those instances only kosher s'chach was placed over the opening of those structures. In this instance, a substance that is not acceptable as s'chach was placed on the roof intentionally.

[In all these cases,] if there are four cubits [or more] from the edge of the kosher s'chach until the wall, it is not acceptable. If there is less than that amount, we view it as though the wall has been made crooked - i.e., the substance that is not acceptable as s'chach is considered part of the wall - Rabbenu Nissim states that this law applies only when the walls reach all the way to the s'chach. Otherwise, it is impossible to consider the non-kosher s'chach to be an extension of the walls. The Tur and the Taz quote more lenient positions and allow such a sukkah, even though the walls do not reach the s'chach.

and it is kosher. - Though the sukkah as a whole is kosher, one may not eat or sleep under the non-kosher s'chach if it is four handbreadths or more in size (Shulchan Aruch, ibid.). The rationale behind this decision is that the non-kosher s'chach is considered to be part of the wall and not part of the s'chach.

This concept is a halachah received by Moses on Mount Sinai. - The latter term refers to a law that was transferred from generation to generation reaching back to Mount Sinai. Nevertheless, there is no mention of - or even direct allusion to - it in the written Torah. See Eduyot 8:7.

What is a small sukkah? - referred to in the previous two halachot and in Halachah 20

Any [sukkah] whose area is no more than seven handbreadths by seven handbreadths. - As explained above, if there are three handbreadths or more of non-kosher s'chach in one place, the principle of l'vud cannot apply. Hence, the sukkah is not kosher, because it lacks the minimum amount of s'chach (Sukkah 17a). However, if there is less than that amount of non-kosher s'chach, the non-kosher s'chach is included as part of the sukkah and is counted as part of its minimum size (Shulchan Aruch, ibid.).

[What is meant by] a large one? Any [sukkah whose area is large enough] that seven handbreadths by seven handbreadths of kosher s'chach will remain besides the s'chach which is not acceptable. - Since it is of sufficient size, it will be disqualified only when it is divided in half by a significant portion of non-kosher s'chach, or when it is too far, i.e., more than four cubits, removed from the walls.

If one used as s'chach substances that were acceptable as s'chach and substances that were not acceptable as s'chach, and placed them alongside each other, leaving no place with non-kosher s'chach more than three handbreadths in area - so that even in a small sukkah, all the conditions mentioned in the above halachot are met, there is a further requirement before the sukkah is considered kosher.

[the following rules apply:] If the total of the kosher s'chach exceeds that of the non-kosher s'chach, it is kosher. - This concept can be derived from the Mishnah (Sukkah 1:8): "If someone places iron staves or the frames of a bed as the roof of his sukkah, it is kosher, provided there is an equivalent amount of empty space."

In his commentary on that Mishnah, the Rambam emphasizes that the word "equivalent" should be interpreted loosely, since there must be more kosher s'chach than the non-kosher s'chach.

If there was an exactly equal amount of both substances, it is not acceptable - This decision has raised questions from all authorities. Though the Rambam's decision is based on Sukkah 15a, Eruvin 15b states that a divider whose open portion is as great as its closed portion is considered to be a divider. Indeed, the Rambam himself quotes that decision in Hilchot Shabbat 16:16. If so, why does he not follow the same principle in this instance as well?

The Kessef Mishneh explains that the Rambam's decision is based on the fact that there is no way that there will not be some tiny open spaces within the kosher s'chach of a sukkah. Accordingly, even if the kosher s'chach is equal in area to the non-kosher s'chach, the tiny spaces between the kosher s'chach will tip the balance in favor of the non-kosher s'chach.

The Shulchan Aruch, Orach Chayim 631:8 quotes the Rambam's decision as halachah, but adds as a reason (a quote from Rabbenu Tam's text of Sukkah 15b): "for it is impossible to be exact." This implies that were it possible to know that the kosher s'chach is exactly equal to the non-kosher s'chach, it would be acceptable. See also commentary to Halachah 19.

even though there is not a single place which has three handbreadths [of non-kosher s'chach] - in a small sukkah, or four handbreadths in a large sukkah.

If one spread a cloth above [the s'chach] - for added shade (Sukkah 1:3)

or spread one below it to catch [the leaves] which fall - the bracketed additions are based on the Rambam's commentary on that Mishnah.

it is unacceptable. - The cloth nullifies the presence of the kosher s'chach above or below it.

(Tosafot explains that as long as the sukkah has sufficient s'chach without the cloth, the cloth will not necessarily nullify the presence of the kosher s'chach. However, the majority of the halachic authorities and the Shulchan Aruch, Orach Chayim 629:19 do not accept this view.)

However, once the cloth is lifted away, the kosher s'chach is acceptable without any further activity. (See Ramah, Shulchan Aruch, Orach Chayim 626:3.) Thus, a roof can be constructed to protect a sukkah from rain, provided it is removed while the sukkah is being used.

If one spread it [under the s'chach] as a decoration, it is kosher. - for a decoration is considered to be an extension of the article it adorns.

Similarly, if one covered the sukkah with s'chach as required by law and adorned it - Rabbenu Manoach emphasizes how the s'chach should be set in place before the decorations. Otherwise, they could be considered as intervening substances.

with various types of fruit, delicacies, and articles - Sukkah 10a describes the decoration of a sukkah with tapestries, nuts, pomegranates, grapes, and flasks of wine, oil, and flour.

which hang from either the walls or the s'chach as a decoration, it is kosher. - and one is permitted to eat and sleep under the decorations.

Sukkah decorations do not reduce its height - i.e., if the inner space of the sukkah is more than twenty cubits high and the sukkah is therefore not acceptable (Chapter 4, Halachah 1), the presence of the decorations is not considered significant to reduce that space to the legal requirements.

Alternatively, if the sukkah is very low and the decorations reduce its inner space to less than ten handbreadths, it is still kosher. (See Halachah 2 with regard to branches.) They are considered to be part of the s'chach, and the space they take up is not taken into account (Kessef Mishneh, Rabbenu Manoach).

but they do reduce its width. - The Bach (Shulchan Aruch, Orach Chayim 639) explains that since we are forbidden to use these adornments throughout the holiday, they are considered to be a permanent part of the sukkah. Thus, the sukkah must have a full seven by seven handbreadths of open space besides them.

If the sukkah decorations are four handbreadths or more - as mentioned frequently above, four handbreadths constitutes a significant space

removed from the roof - they are considered to be non-kosher s'chach, and if they are of the size mentioned in Halachot 13 and 14...

it is unacceptable, because it is as though a person who sits there is not sitting under the s'chach, but rather under the decorations, which are foods and utensils that are not acceptable as s'chach. - See Chapter 5, Halachot 1 and 2.

The Taz (627:5) cautions against hanging any decorations more than four handbreadths away from the s'chach regardless of how small they are.

The [following rules apply when the] s'chach has open spaces through which the sky can be seen: If the area of the open spaces is equivalent to - and of course, if it is more than

that of the space covered by s'chach, it is not acceptable, because - Although the sukkah should be acceptable as long as the covered portion is equal to the open portion, in this situation...

the portion exposed to the sun will be greater than the shaded portion. - Sukkah 22b explains that light spreads out. Accordingly, even though on the roof the portion covered by s'chach is equal to the uncovered portion, on the ground the area exposed to the sun will be greater than the shaded area. See also the Rambam's commentary on the Mishnah, Sukkah 1:1.

Whenever the portion exposed to the sun is greater than the shaded portion, it is not considered as s'chach. - As mentioned in Halachah 9, a sukkah must be constructed for the purpose of shade. If the portion exposed to the sun is greater than the shaded portion, it obviously does not serve that purpose.

If the s'chach exceeds the open space, it is kosher. - On the surface, the Rambam's choice of phraseology is slightly inexact, because everything depends on the amount of shade on the ground.

When does the above apply? When there is no one open space - To disqualify the sukkah, the empty space must extend across the entire span of the sukkah or create a place large enough for a person to stand in (Tosafot, Sukkah 17a; Ramah, Shulchan Aruch, Orach Chayim 632:2).

Furthermore, if the sukkah area is more than seven handbreadths by seven handbreadths in addition to the open space, the remaining covered area of the sukkah is kosher.

of three handbreadths - Any space less than three handbreadths can be considered to be part of the s'chach on the basis of the principle of l'vud.

Though the sukkah as a whole is kosher, it is forbidden to eat or sleep under the open portion (Shulchan Aruch, Orach Chayim 632:2).

However, if there is an open space of three handbreadths - whether in the center - i.e., an empty space cutting the sukkah in two

or at the side - i.e., an empty space that runs from one corner of the sukkah to the other. Rashi, on Sukkah 17a, explains that the concept of דופן עקומה, by which non-kosher s'chach is considered an extension of the wall, does not apply in this instance. Since it is merely empty space, it cannot be considered to be an extension of the wall.

It must be emphasized that we are speaking about a sukkah with only three walls. If the sukkah has four walls, but there is an empty space between the s'chach and the fourth wall, the sukkah as a whole is kosher.

it is unacceptable until one reduces [the space] to less than three.

If one used substances that were not acceptable as s'chach - e.g., pillows and blankets - to reduce the space, it is kosher - Non-kosher s'chach and open space are two different halachic categories. They have different measures with which they each disqualify a sukkah, and combinations of the two are not considered to be a single entity. Thus, if there is an open space three and a half handbreadths wide, one may correct the sukkah by putting one handbreadth of non-kosher s'chach in its place. (See the Shulchan Aruch, Orach Chayim 632:3.)

if the sukkah is large. - The terms "large" and "small" are explained in Halachot 13-15.

If it is a small sukkah, it is not acceptable - because the sukkah has less than seven handbreadths by seven handbreadths of kosher s'chach.

unless [the space] was reduced with a substance that is acceptable as s'chach.

When the shaded portion of most of the sukkah exceeds the portion exposed to the sun, although in the lesser part of the sukkah the portion exposed to the sun exceeds the shaded portion - i.e., there are two portions of the sukkah, one which is mostly shaded and one which is mostly exposed to the sun.

because - when the sukkah is taken...

as a whole the shaded portion exceeds the portion exposed to the sun, it is kosher - and one may eat and sleep in the part of the sukkah where the portion exposed to the sun exceeds the shaded portion (Magen Avraham 631:1). The Ramah quotes a more stringent opinion which forbids using the portion with more sun if it is seven handbreadths by seven handbreadths in area.

The proper way - Shulchan Aruch HaRav (631:5) uses the expression לכתחילה - i.e., one should set out to construct a sukkah in this manner.

is that s'chach should be thin, so that the large stars can be seen through it. - From the Jerusalem Talmud, Sukkah 2:3, the source for this statement, it appears that the expression "large stars" means stars large enough to be seen during the day.

However, even though it is thick - like [the roof of] a house - and stars cannot be seen through it - The latter expression is quoted from the Mishnah, Sukkah 2:2.

it is kosher. - Shulchan Aruch HaRav (631:5) uses the expression בדיעבד (after the fact), implying that it is not desirable to construct a sukkah in this manner. Nevertheless, the Mishnah Berurah (631:5) quotes many Ashkenazic authorities who tend toward making the s'chach thick.

The above applies only with regard to placing the s'chach. However, afterwards, even when the s'chach is thick, a person should have no compunctions about using such a sukkah.

Though thick s'chach is kosher, the Magen Avraham 631:2 notes that if it is so thick that rain will not enter the sukkah, the sukkah is unacceptable, because then it resembles a house and not a temporary dwelling made for shade.

If the s'chach was uneven - Sukkah 22a questions: "What is the meaning of the word מדובללת used by the Mishnah?" Shmuel (whom the halachah follows) replies: "One reed going upward and one reed going downward."

i.e., some of it high and some of it low - it is kosher - Even though there will gaps in the s'chach and during certain times of the day, when the sun shines at an angle, the portion of the sukkah exposed to the sun will exceed the shaded portion (Ramah, Orach Chayim 631:5).

provided there is less than three handbreadths between the upper and lower [portions of the s'chach]. - As explained previously, any distance less than three handbreadths is not significant because of the principle of l'vud.

If the upper portion [of the s'chach] is a handbreadth - by a handbreadth, the minimum size of a roof. (See Chapter 4, Halachah 7.)

or more wide, even though it is more than three handbreadths above [the lower portion], we consider it to be descending and touching the edge of the lower portion. - This principle, referred to by Sukkah 22a as חבוט רמי - literally, "cast it down" - is one of the leniencies followed as a halachah received from Moses on Mount Sinai. It allows this uneven roof to be considered to be a single straight entity. The same principle is also applied in Hilchot Shabbat 15:25 and Hilchot Tum'at Meit 16:5.

[This applies] provided it is aligned opposite the edge of the lower portion. - i.e., that the upper portion could be lowered into the space left open by the lower portion. However, if it would not fit exactly in between the spaces, this principle does not apply (Kessef Mishneh). The Lechem Mishneh, noting the Rambam's decision in Hilchot Shabbat, explains that even if the lower space is wider than the upper portion, as long as they do not overlap, it is acceptable.

The Merchevat Hamishneh explains that the law differs here from Hilchot Shabbat, because there is a principle that two halachot received from Moses on Mount Sinai cannot be used simultaneously to have a sukkah considered to be kosher.

In the Shulchan Aruch (Orach Chayim 631:5), Rav Yosef Karo quotes the opinion he stated in the Kessef Mishneh. However, Shulchan Aruch HaRav (631:7) and others follow the view of the Lechem Mishneh.

When a person constructs one sukkah on top of another sukkah, the lower one is unacceptable. - Sukkah 9b explains that the verse which commands us to dwell in sukkot (Leviticus 23:42) spells the word - סכת - omitting the letter ו, which is usually used. On that basis, the Sages explained that a single structure may be used for one sukkah, but not for two. Of the two, the lower sukkah is disqualified because...

It is considered as though it had been constructed in a house. - since the floor of the upper sukkah is its roof, it may not be considered to be s'chach, because it was not placed there for purposes of shade alone, nor can the lower sukkah be acceptable because of the s'chach of the upper sukkah, for the floor intervenes between them.

[However,] the upper one is kosher - There is no reason that the presence of the lower sukkah should disqualify it.

When do we say that the lower one is unacceptable? When the inner space of the upper sukkah is ten handbreadths or more [high] - the minimum height of a sukkah, as explained in Chapter 4, Halachah 1.

and the roof of the lower sukkah is strong enough to hold the pillows and covers of the upper sukkah - Otherwise, the upper sukkah is not fit to dwell in. Though a sukkah is only a temporary dwelling, it must be fit to be used for all the purposes for which one uses one's home, as explained in Chapter 6, Halachah 5.

even if that is done with difficulty. - i.e., even if the floor of the upper sukkah shakes when pillows and covers are placed on it (Rambam's commentary on the Mishnah, Sukkah 1:2).

However, if the inner space of the upper sukkah is less than ten handbreadths [high], or the roof of the lower sukkah is not strong enough to hold the pillows and covers of the upper sukkah, even with difficulty - and thus, is unfit to be used.

even - The use of this word is questionable. It implies that both sukkot, the upper and the lower one, are kosher. The Kessef Mishneh states that if the upper sukkah is not fit to dwell in, it is not kosher, and therefore recommends striking the word "even" from the text. Though the Lechem Mishneh attempts to justify the use of the term, his arguments seem forced. However, it must be noted that most manuscripts and printings of the Mishneh Torah as well as the Rambam's and most other texts of the source for this halachah - the Mishnah, Sukkah 1:2 - include this word.

the lower sukkah is kosher. - for the reason that since its roof is of no functional purpose, it is not considered an intervening substance between the sukkah and the upper s'chach.

This applies provided the height of both together does not exceed 20 cubits - the maximum height of the sukkah, as stated in Chapter 4, Halachah 1.

since [use of] the lower sukkah is permitted because of the s'chach of the upper one. - In the Kessef Mishneh - and also in the Shulchan Aruch (Orach Chayim 628:1) - Rav Yosef Karo explains that this applies only when the s'chach of the lower sukkah is not substantial enough to allow the use of the sukkah. However, if the s'chach of the lower sukkah alone produces enough shade to permit the use of the sukkah, it is kosher even though the s'chach of the upper sukkah is more than 20 cubits high.

He continues to explain that even though the presence of non-kosher s'chach nullifies the kosher s'chach below it, that applies only when the substance used is by nature not acceptable for use as s'chach. In this instance, the s'chach of the upper sukkah is fit to be used; the only difficulty is its position: its placement above the maximum height of the sukkah.

(Though this concept is found in Tosafot, Sukkah 9b, no allusion to it appears in the Rambam's statements. Indeed, the simple meaning of the Rambam's words implies the very opposite. Furthermore, in his commentary on the Mishnah [Sukkah 1:1], the Rambam explains that the reason s'chach placed higher than 20 cubits is unacceptable is that it makes the sukkah into a permanent dwelling. Thus, according to the Rambam, such s'chach can be compared to the boards of a house, which though originally kosher for use as s'chach, are disqualified because they became part of a permanent structure.)

A bed [with a canopy placed] inside a sukkah: If [the canopy] is more than ten handbreadths high - the minimum height for a dwelling to be considered to be an independent structure (Sukkah 20b).

In this and the following instances mentioned in this halachah, the ten handbreadths are measured from the ground to the canopy (Shulchan Aruch HaRav 627:2-3; Mishnah Berurah 627:5).

a person who sits under it does not fulfill his obligation - The Mishnah, Sukkah 2:1 relates:

An incident occurred concerning Tavi, Rabban Gamliel's slave. He would sleep under a [canopied] bed [in the sukkah]. Rabban Gamliel told the Sages: "See my slave, Tavi. He is well-learned and knows that slaves are free of the obligation of [dwelling in] the sukkah. Hence, he sleeps under a bed."

for it is considered to be a sukkah - with non-kosher s'chach

within a sukkah. - even if it has no walls (Shulchan Aruch HaRav 627:1)

Similarly, a canopy - placed over a bed

with a roof - even as small as a handbreadth: - As mentioned frequently above, a handbreadth is the minimum measure of a roof.

If it is ten handbreadths high, one may not sleep - or perform any other activity required to be performed in a sukkah. (Perhaps the Rambam mentions sleeping because it is an activity that may be performed only within a sukkah. Even a short nap should not be taken outside the sukkah. In contrast, a snack may be eaten outside a sukkah.)

under it in a sukkah. - for the same reasons mentioned above.

By the same token, if one sets up four pillars and spreads a sheet over them, if they are ten [handbreadths high], they are considered to be a sukkah within a sukkah. - Hence, we are forbidden to use the space below it as a sukkah.

This halachah depends on the Rambam's interpretation of the Mishnah, Sukkah 1:3. However, Tosafot, Sukkah 10b and the Shulchan Aruch (Orach Chayim 627:3) interpret the passage differently and forbid spreading a canopy over bedposts which are permanently affixed to the four corners of a bed, even if the canopy is less than ten handbreadths above the ground.

In contrast, should one spread a sheet over two pillars - Tosafot (ibid.) and the Shulchan Aruch (ibid.) differ with this decision as well, and explain that if these pillars are ten handbreadths high and permanently affixed to the bed, it is forbidden to spread a sheet over them.

or [use] a canopy that has a roof of less than a handbreadth - If the canopy is not permanently affixed to the bed, even Tosafot and the Shulchan Aruch will permit its use.

no matter how high they are - i.e., even if they are more than ten handbreadths high.

it is permitted to sleep under them within a sukkah. - Sukkah 19a relates that Abbaye found Rav Yosef sleeping in a canopied bed in the sukkah. The latter explained that the canopy he was using was permitted because it did not have a roof.

They are not considered to be a sukkah within a sukkah, because they do not have a roof. - As stated in Chapter 4, Halachah 7, such structures are not acceptable for use as a sukkah. Hence, they also cannot disqualify a sukkah.

A borrowed sukkah is fit [to be used on the holiday]. - Although, as stated in Chapter 8, Halachah 10, a person cannot fulfill the mitzvah of lulav as prescribed by the Torah with a lulav belonging to a colleague, that concept does not apply with regard to a sukkah.

Sukkah 27b explains the derivation of this concept as follows: Leviticus 23:42 states: "Every citizen of Israel shall dwell in sukkot." The latter word is written סכת, implying one sukkah. This prompted our Sages to declare: "All Israel are fit to dwell in a single sukkah."

In his commentary, Rashi explains that the cost of such a sukkah would not be high enough to require every individual to pay a penny's worth. Hence, we must assume that some people would be using a borrowed sukkah, and, nevertheless, our Sages said that it was kosher.

Similarly, a stolen sukkah is also fit [for use]. - There is a slight imprecision with the Rambam's statements. A stolen object which the thief is obligated to return cannot be used to perform a mitzvah, because it is considered a mitzvah that came about through a sin (מצוה הבאה בעבירה). However, in the instances cited by the Rambam, the sukkah itself is never considered stolen property. Hence, the use of such a sukkah is not forbidden. However, in a number of instances (see below), the sukkah itself is considered to be stolen property and must be returned. Hence, it cannot be used to fulfill the mitzvah.

What does the latter imply? If a person attacked a colleague, forced him to leave his sukkah, stole it, and dwelled in it, the attacker has fulfilled his obligation, because landed property cannot be stolen. - Hilchot Gezeilah 8:14 relates that "landed property is never acquired by a thief, but rather remains in the possession of its owner forever."

Since the sukkah is built on the land, it is considered part of the property and the above rule applies to it as well. Thus, the sukkah is still considered to be the property of its original owner and the thief is viewed as merely "borrowing" the sukkah from him. As mentioned above, use of a borrowed sukkah is permitted.

[Similarly,] if he stole wood and made a sukkah from it, he has fulfilled his obligation - Sukkah 31a relates that a woman once came to Rav Nachman complaining that the exilarch's servants had stolen wood from her to build his sukkah.

Rav Nachman answered that they had, nevertheless, fulfilled their obligation...

because the Sages ordained that the owner of the wood is entitled only to the monetary worth of the wood - but not the wood itself. Thus, the sukkah itself is the property of the thief. Though he is obligated to pay the owner for his wood, that obligation does not prevent the sukkah from being considered as his.

Hilchot Gezeilah 1:5 explains this principle by stating:

Anyone who steals is obligated to return the stolen property itself... If it was lost or changed, he is obligated to return its monetary value...

Even if one steals a beam and builds a mansion [using it], since [the beam] has not been changed, the Torah law would require him to destroy the entire building and return the beam to its owner.

Nevertheless, the Sages instituted a decree [to encourage] those who repent; they ordained that all that is necessary is for him to return [the beam's] monetary value, and thus he will not forfeit his building.

Rabbenu Manoach asks: Since the mitzvah of sukkah is commanded by the Torah, and Torah law regards these boards as stolen, how can the Sages' decree change their status in this context?

He explains that, as implied by the principle הפקר הפקר בית דין, the Torah has granted the Sages the right to determine the status of property. Their decree can alter entirely a person's rights to its title. Thus, in the present case, since Rabbinic law entitles the thief to use of the boards, he is permitted, according to Torah law, to use them as a Sukkah.

The Magen Avraham (637:5) writes that if the thief refuses to pay for the wood, it is considered to be the property of its original owner, and the thief does not fulfill his obligation.

Even if one stole boards and merely put them in place without attaching them or changing anything about them, he has fulfilled his obligation. - This is a special leniency granted out of respect for the mitzvah of sukkah (Sukkah, ibid.). Since the thief has not made any changes in the wood itself or built a permanent structure from it, the Rabbinic decree mentioned above would not apply. Thus, during the rest of the year (and even in this case, after the Sukkot festival), the wood would have to be returned. During the festival, the Sages considered it to be the property of the thief and he is allowed to use without any constraints throughout the festival (Hilchot Gezeilah, ibid.).

Nevertheless, in his Kessef Mishneh and in his Shulchan Aruch (Orach Chayim 637:3), Rav Yosef Karo gives two examples of a stolen sukkah which one is forbidden to use: a sukkah that had been constructed on a ship or one that had been constructed on a wagon. Since the thief did not build anything, the abovementioned Rabbinic decree does not apply; nor are they affixed to land, and hence the principle that landed property cannot be stolen is not relevant.

If a person constructs his sukkah in the public domain - Though the Jewish inhabitants of the city would surely not object to use of public property for this purpose, the gentile inhabitants of the city would. Since they also have a share in this property, building a sukkah there is equivalent to stealing from the public (Magen Avraham 637:3).

Nevertheless, since the theft of land is involved...

it is acceptable - for the reasons mentioned above. Note the Magen Avraham, ibid. and the Bi'ur Halachah, who discuss whether or not it is permitted to recite a blessing when using such a sukkah.