Rambam - 1 Chapter a Day

The rationale for this ruling is the principle of migo. If the husband’s statements were untrue and his intent were merely to free his wife from the obligation of yibbum, he would not have to lie. Instead, he could give her a get (Bava Batra 134b).
See also the Shulchan Aruch (Even HaEzer 156:6) and commentaries, which mention other opinions regarding whether this ruling applies when the prevailing presumption is that the man is childless, when the prevailing presumption is that he has brothers, or when witnesses testify that he has brothers.

I.e., when the prevailing presumption is that he does not have a brother, and hence his wife would not be obligated to perform yibbum.

Even though the statements are being made at the time of the person’s death, when it is unlikely that he would lie, we still suspect that he is speaking falsely to spare his wife the difficulty of yibbum or chalitzah.

One might assume that, as in Halachah 1, the husband’s statements would have been accepted based on the principle of migo. For in this instance as well, the husband could free his wife from yibbum by giving her a get. Nevertheless, our Sages explain that the principle of migo does not have the power to counteract a prevailing presumption.
Still, even if the prevailing presumption is that a person has brothers, his word is accepted if he says that he has sons. The rationale is that, in this instance, his statements are not contradicting the prevailing presumption, but rather introducing a new factor (Beit Shmuel 157:9).

There is a difference of opinion among the Rabbis whether or not this rumor has to be substantiated in a court. The Maggid Mishneh interprets the Rambam’s opinion as being that even a rumor that is not substantiated should be taken into consideration. Needless to say, in the contemporary era, when communications have advanced and travel is easier, this question is far less significant than in previous ages.

See Hilchot Nachalot 4:1.

If the woman is married, there is no question regarding the Rambam’s ruling, for we presume that by and large, she engaged in relations with her husband. If she is single, the matter is more complex.
In this context, the commentaries draw attention to the Rambam’s ruling in Hilchot Terumot 8:14, which states that when a priest had relations with a woman and she became pregnant, she is allowed to partake of terumah for the sake of her child. This indicates that we assume that she was impregnated by that priest.
As indicated by the Rambam’s wording in Hilchot Terumot and in Hilchot Issurei Bi’ah 15:17-18, the matter depends on the woman’s reputation. If she is known to be promiscuous, we consider the possibility that she was impregnated by another man. If, however, everyone presumes that she engaged in relations only with this man, he is considered to be the father of the child (Maggid Mishneh).
Nevertheless, the Shulchan Aruch (Even HaEzer 156:9) quotes the Rambam’s wording without making this distinction. See the Beit Shmuel 156:15.

Lest the child have been fathered by another man and the deceased in fact be childless.

Lest the child have been fathered by the deceased, in which case relations with his brother would be prohibited.

Rabbenu Asher differs with the Rambam regarding this matter and maintains that The testimony of one witness is not acceptable with regard to the death of a yavam. Although the Rama (Even HaEzer 158:3) quotes his opinion, many Ashkenazic authorities recommend leniency. (See Beit Shmuel 158:2.)

The Ra’avad and Rabbenu Asher differ with the Rambam with regard to this point, for unlike the death of a person, the birth of a child is not a matter that will surely become undeniable public knowledge. The Shulchan Aruch (Even HaEzer 156:8) quotes the Rambam’s opinion, while the Rama follows the other view.

In Hilchot Gerushin, Chapters 12 and 13.

See Hilchot Gerushin 12:16, which states that the statements of a woman’s mother in law, the daughter of her mother-in-law, [her husband’s] other wife, her yevamah (i.e., the wife of her husband’s brother) and her husband’s daughter are not accepted with regard to her husband’s death, because the prevailing presumption is that they hate each other.

I.e., the women are married to two brothers. Thus each one is considered the yevamah of the other.

I.e., the testimony of each woman is accepted with regard to the death of her own husband. With regard to the death of her yavam, by contrast, the only testimony is that of her yevamah, and that testimony is not accepted.

And with regard to the death of her yavam, there is no testimony that is acceptable to the court.
Even if the woman actually remarries, at which point, it would be likely to assume that her husband is dead, her yevamah is still prohibited. Our Sages feared that a woman would risk ruin in both this world and the next, in order to cause her foe to be forbidden to her husband.

See Hilchot Gerushin 12:15.

And neither has witnesses to support her testimony.

For she is dependent on the testimony of her yevamah, as above.

For her authorization to remarry does not depend on whether or not her yavam is alive.

Or chalitzah.

I.e., there were only three brothers. Since the death of the first two brothers was never verified adequately to allow these women to marry freely, the original prohibition applying to them remains in force.

For her marriage and divorce releases each of the women from their obligation to their missing yavam.

The punishment — lashes — is lesser, and the woman’s children are not considered illegitimate.

Having relations with another man while married, by contrast, is a prohibition punishable by execution by the court, her children are considered illegitimate, and it brings severe retribution in the world to come. Because the prohibition against marrying while under obligation to a yavam is less severe, our Sages feared that the woman might lie about the yavam’s death and transgress this prohibition.

It is forbidden for a husband to marry his wife’s sister while his wife is alive. Our Sages feared that the second sister or the husband may desire to give false testimony, so that they can marry.

I.e., generally, the testimony of two witnesses is required with regard to matters involving marriage and divorce. As mentioned in the concluding passage of Hilchot Gerushin (cited in the notes on Halachah 6), in order to allow a woman to remarry, leniency is granted and merely on the testimony of one witness. In this instance, however, there is no difficulty in the man’s or the woman’s remarrying; the only difficulty is that they cannot marry each other. In such an instance, our Sages were not willing to extend leniency.
[There is a slight difficulty when comparing the Rambam’s statements here to his statements at the conclusion of Hilchot Gittin. As explained by the Noda B’Yhudah (Even HaEzer, Volume I, Responsa 27 and 33), the Rambam’s wording indicates that, according to Scriptural Law, with regard to a point of fact that can be verified, it is not necessary for two witnesses to testify, and the statements of one witness are sufficient. The leniency granted your Sages was to accept the testimony of women, relatives and others whose testimony would not ordinarily be accepted. Here, however, the Rambam is stating (as he does in Hilchot Edut 5:2) that the acceptance of the testimony of a single witness is a leniency of Rabbinic origin. (See the Responsa of the Rivash, Responsum 181.)]

I.e., based on the premise stated in the first clause of the previous halachah.

For the prevailing presumption when she departed was that she would be obligated to perform yibbum if her husband dies.

The prevailing presumption when she departed was that she would not be obligated to perform yibbum if her husband dies. It is only because of her own statements that we might suspect that she is required to do so. Therefore, her statements are sufficient to offset this suspicion.

We suspect that perhaps she is lying in order to marry her brother-in-law.

I.e., were it not for her statement that her son died first, she would be permitted to marry without any restrictions. Because we give her statements some credence, we require her to perform chalitzah.

I.e., were it not for her statement that her son died after her husband, she would be required to perform yibbum. We do not accept her word to the extent that we allow her to marry without restrictions. Nevertheless, we give her statements some credence and forbid the performance of yibbum, lest in fact there be no obligation to do so.

A woman who is born from a relationship that is forbidden to a priest, but not to an Israelite.

In which case, the chalitzah does not make any difference, for the woman was forbidden to the priesthood regardless

In which case, there is no apprehension of witnesses coming.

For according to her testimony, she is forbidden to do so.

Note the discussion of this ruling by the Beit Shmuel 156:17, and the opinion mentioned there that this ruling applies only when there were witnesses who testified that the woman’s husband and son both died. Otherwise, the woman’s word would be accepted based on the principle of migo — i.e., if she desired to lie, she could have said that her son was still alive.

This law applies even if the second wife was not pregnant when she left. Our Sages considered the possibility of the woman becoming pregnant as a reasonable probability.

See Chapter 1, Halachah 19.

We do not consider the possibility that the woman was impregnated by her husband before he departed on the journey and did not realize this until he had already departed.

For even if we presume that the mother-in-law will become pregnant, it is more probable that she will miscarry or give birth to a girl (in which cases, the mitzvah of yibbum would not apply) than that she bear a son (Beit Shmuel 157:11).

For according to the testimony she was given, her husband was survived by a son, and the mitzvot of yibbum and chalitzah do not apply.

In which case her husband would have died without children, and she would be obligated to perform yibbum or chalitzah.

See Chapter 2, Halachah 18.

For it is only when a child is born from forbidden relations that are punishable by karet that this status is incurred (Yevamot 49a).

For her relations with her brother-in-law were prohibited by a transgression punishable by karet. The fact that she violated this prohibition unwittingly does not change the status of her children.