Gemara

(Mishnah): If Reuven says 'this is my son', he is believed. If he says 'this (Ploni) is my brother', he is not believed. Reuven and Ploni divide what Reuven inherited from his father. When Ploni dies, Reuven gets back what Ploni took from Reuven's share. If Ploni had received property from another place, all the brothers share it.

(Rav Yehudah): Reuven is believed (to say 'this is my son') to exempt Reuven's wife from Yibum.

Question: We already learn this from a Mishnah!

(Mishnah): If Reuven said just before he died 'I have sons', he is believed. If he said 'I have brothers', he is not believed.

Answer: There, he is Muchzak not to have brothers (he is believed because even without his words, the Chazakah is that his wife will be permitted when he dies). Here, he is believed even if he is Muchzak to have brothers.

(Rav Yosef): Rav Yehudah taught that he is believed because he could exempt her from Yibum if he wants by divorcing her.

135a - Question: When Reuven said 'this (Ploni) is my brother', what did the other brothers say?

If they admit 'he is our brother', they all divide equally! (If not, after Ploni dies, why do they share what Ploni received from elsewhere?)

Kidushin 64a (Mishnah): If Reuven said just before he died 'I have sons', he is believed. If he said 'I have brothers', he is not believed.

Suggestion: He is believed to permit, but not to forbid. Our Mishnah is not like R. Noson:

(Beraisa - Rebbi): If at the time of Kidushin, Reuven said 'I have no children', and at the time of death he said 'I have children', or at the time of Kidushin he said 'I have no brothers'; and at the time of death he said 'I have brothers', he is believed to permit, but not to forbid;

R. Noson says, he is believed even to forbid.

Rejection #1 (Rava): The Beraisa is different. Since at the time of death he contradicted what he said earlier, surely he is not lying.

Objection (Abaye): If in the Mishnah, even though he doesn't contradict himself, he is not believed to forbid. All the more so in the Beraisa, when he contradicts himself, he should not be believed to forbid!

Rejection #2 (Abaye): In the Mishnah, the Chazakah was that he had no children or brothers (so his wife will not fall to Yibum). He is believed to say that he has children, for this supports the Chazakah, but not to say that he has brothers, which opposes the Chazakah. In the Beraisa, the Chazakah was that his wife will fall to Yibum. He would not lie (at the time of Kidushin) to exempt her from Yibum, for he could divorce her. Rebbi holds that this reasoning (he need not lie) is like witnesses, so it overturns the original Chazakah. R. Noson holds that this reasoning is like a Chazakah. It does not override the original Chazakah (so he is believed to forbid at the time of death).

Rishonim

Rif and Rosh (8:39): One is believed to say that he has a son even if he is Muchzak to have brothers.

Rambam (Hilchos Yibum 3:1): If Reuven said 'this is my son' or 'I have sons', he is believed, and he exempts his wife from Chalitzah and Yibum.

Rambam (2): If he said 'this is my brother' or 'I have brothers', he is not believed to forbid his wife and force her to do Chalitzah or Yibum with the Yavam (before remarrying), for he intends to forbid her after his death.

Rosh (8:39): Surely the latter Mishnah cited discusses exempting his wife from Yibum. If it discussed inheritance, there would be no reason to believe him about having sons, but not to believe him about having brothers.

Poskim

Shulchan Aruch (EH 157:6): If Reuven was Muchzak not to have brothers, and he said 'I have brothers' he is not believed. If a man came and said 'I am his brother', he is not believed.

Beis Yosef (DH v'Chosav Rabeinu): R. Yerucham says that even Rebbi holds that he is believed to say that he has sons when there is a Chazakah that he has brothers, but not if there are witnesses that he has brothers.

Gra (15): The Gemara assumes that when Reuven said 'this (Ploni) is my brother', Ploni agreed. The Gemara (135a) asked 'what do the other brothers say'. It did not ask what Ploni says in the Reisha, when he gets half of Reuven's share. Even so, Ploni is not believed (against a Chazakah) regarding Yibum.

Shulchan Aruch (ibid): Even if one witness (Rema - or relative) testifies that he is his brother, he is not believed to remove the Chazakah of Reuven's wife (that she will be permitted when Reuven dies).

Gra (16): The Shulchan Aruch (YD 127:3) rules that one witness is not believed about Isurim to be stringent. This is like the Rosh (Gitin 5:8)

Darchei Moshe (6): The Mordechai (Yevamos 58,59) says that we do not heed testimony of relatives that he is a brother, because he was not Muchzak to have brothers.

Beis Shmuel (8 and Gra 17): The text of the Rema should say 'relatives', like it says in Darchei Moshe.

Beis Yosef (DH v'Chosav ha'Rosh): A case occurred in which Leah married David. We never heard that David had a brother, but Levi's brother went abroad and found a man who said that he is David's brother. David died. The Rosh (52:5) ruled that she keeps her Chazakah, and may remarry. All agree that a husband is not believed to forbid her against her Chazakah. Even though the Halachah follows Rebbi, Rebbi says only that he is believed to permit her against her Chazakah. All the more so, her brother is not believed to forbid her. We would not be concerned even for a Kosher witness against her Chazakah! Gitin 54b teaches that one witness is not believed to forbid against Chezkas Heter (unless he is able to make the matter Asur). Also, her brother only said that Ploni claimed to be David's brother. If Ploni came and said so, he would not be believed regarding money, and not regarding Isur. We are concerned only when there is a Kol (rumors) that (two) witnesses know that he has a brother.

Shulchan Aruch (YD 127:3): One witness is believed to be lenient about Isurim, but not to be stringent.

Rema: Some say that one witness is believed even to be stringent about something without a Chazakah for Heter or Isur.

Beis Shmuel (156:7): In YD, the Rema says that one witness is believed when there is no Chazakah. Here, since he is not Muchzak to have brothers, it is as if she is Muchzekes that she will not fall to Yibum. Kidushin 64a considers this like Chezkas Heter. However, this is difficult for the Nimukei Yosef (Bava Basra 61b DH Leyorsho), who says that (one is believed when there is no Chazakah. This shows that he holds that) no Chazakah for children is not like a Chazakah that he has no children. If so, one witness should be believed! Rashi and the Ran (Kidushin 64a DH d'Lo and 27b DH Omar) connote that if he did not say 'I have sons', even if he did not say that he has brothers, and he was not Muchzak to have either, if someone comes and says 'I am his brother', we are concerned. (They say that 'he is believed to say that he has sons' means that we will not be concerned if this happens.) If so, all the more so one witness can forbid! We can say that the Nimukei Yosef agrees. He, Rashi and the Ran hold that one is believed to say 'I have sons' even if witnesses say that he has brothers. Some Poskim say that he is not believed (EH 156:6), but only because they hold that it is considered Vadai that she wil fall to Yibum.