Gemara

Nedarim 90b (Mishnah): At first, if a woman said to her husband 'let Shamayim judge between us', Beis Din would force him to divorce her and pay her Kesuvah. Chachamim changed this, lest women use this claim in order to marry someone else. Rather, he tries to appease her.

(Rava): The Mishnah Rishonah believes one who says that she was defiled only because she would not lie to disgrace herself.

Question (Rav Mesharshiya): Mishnah Rishonah believes her when she says 'Shamayim is between us', even though this is no disgrace to herself!

Answer (Rava): This means that Eino Yoreh k'Chetz. This is an awesome disgrace to him, she is not so brazen to lie about such a matter.

Question (Mishnah Acharonah): If she says 'Shamayim is between us' she is not believed. This refutes Rav Hamnuna, who believes woman (who says to her husband that he divorced her) because she lacks the audacity to lie to him!

Answer (Rav Hamnuna): The husband knows that he has Bi'ah, but does not know whether or not he is Yoreh k'Chetz, so she is able to lie about this.

Yevamos 64a (Beraisa): If a couple did not have children in 10 years, he must give a Get and a Kesuvah. Perhaps he did not merit to have children through her;

65a (Beraisa): If twice a woman married and did not have children in 10 years, afterwards she may marry only a man who has children. If she married a man without children, she leaves him without a Kesuvah.

(R. Ami): If each of them says that the other is sterile, this is 'matters between the two of them'. She is believed (and receives a Kesuvah). This is because she can tell whether or not he is Yoreh k'Chetz, but he cannot.

(R. Ami): Even if he says that he will marry another woman to prove that he can have children, he must divorce her and pay a Kesuvah. I say that anyone who takes a second wife must grant his first wife a divorce and a Kesuvah.

Rishonim

Rif (Yevamos 20b): A Gaon says that R. Ami's law is like Mishnah Rishonah. We follow Mishnah Acharonah. When she says 'Shamayim is between us' he tries to appease her. Perhaps she seeks to marry someone else. I disagree. R. Ami refers to the Mishnah and Beraisa (Yevamos 64a) that obligate a Get and Kesuvah after 10 years without children. If they argue about the Kesuvah, i.e. each says that the other is sterile, R. Ami believes her if she says Eino Yoreh k'Chetz. Even if she desires another man, in any case we force her to leave him! The Mishnah Rishonah discusses one who seeks to leave before 10 years.

Question #1 (Rosh Yevamos 6:15): How could he seek to exempt himself of a Kesuvah through a Safek claim without any proof?

Answer (Milchamos Hash-m): The case is, he has a Vadai claim, e.g. she emits the semen, and he wants to swear to exempt himself. She says that this is immaterial, for he cannot father children. R. Ami does not discuss within 10 years, for then even without her claim we ignore his claim. If not, the enactment of Kesuvah would be futile! Also, within 10 we are concerned lest she seeks to marry another man.

Question (Rosh): If he has a Vadai claim, it can even be within 10 years. Since she does not seek to be divorced, we are not concerned lest she desires another man!

Question #2 (against Rif - Ba'al ha'Ma'or): Even if he is Yoreh k'Chetz, he must pay a Kesuvah because he did not merit to have children through her! Since he is commanded about Peru u'Rvu, he was punished! R. Ami does not teach about a Kesuvah, rather, whether or not he must divorce her. We believe her that he is sterile, so he need not divorce her. Alternatively, if he fulfilled Peru u'Rvu through a previous wife and she says that now Eino Yoreh k'Chetz and she needs children for her old age, he must divorce her and pay a Kesuvah.

Answer (Milchamos Hash-m): After 10 it is more reasonable to say that she is sterile than to say that he is being punished. If he already fulfilled Peru u'Rvu surely she is being punished. Even if she does not say that she needs children for her old age, we know that she does.

Rambam (Hilchos Ishus 15:8): If she was with him for 10 years without children and he is Yoreh k'Chetz, we attribute the sterility to her. She receives only Tosefes Kesuvah. If Eino Yoreh k'Chetz, the Chazakah is that only he is sterile. When he divorces her she receives the Ikar Kesuvah and Tosefes.

Rebuttal (Ra'avad): She gets only Tosefes only from her third husband. In any case her first two husbands pay her Kesuvah. Perhaps they did not merit to have children from her. I say that she receives Ikar Kesuvah but not Tosefes. He did not intend to add to her Kesuvah in such a case.

Rambam (9): If he says that children are being withheld from her and she says Eino Yoreh k'Chetz, she is believed. Before paying the Kesuvah, he may impose a Cherem Stam on one who claims without really knowing. We leave money, i.e. Ikar Kesuvah, in its Chazakah unless she is sure that Eino Yoreh k'Chetz. She is believed because she feels whether or not he is Yoreh k'Chetz, but he does not.

Magid Mishneh: The Gemara does not mention a Stam Cherem, but the Ge'onim agreed upon this in many cases.

Question (Rosh 15): R. Ami taught that she is believed about 'matters between them', i.e. each says that the other is sterile. If this is after 10 years, even if he is Yoreh k'Chetz he must divorce her and pay a Kesuvah, for he did not merit to have children through her. If it is within 10 years, we should be concerned lest she wants to marry someone else, like the Mishnah Acharonah!

Suggestion: R. Ami discusses when she claims that she needs children for her old age, and the Mishnah is when she does not claim this.

Rejection (Rosh): In any case, R. Ami should be concerned lest she desires another man. Also, the Mishnah Rishonah would not obligate a Get and a Kesuvah if she did not claim this! At the end of our Sugya, we obligate a Get and a Kesuvah when she makes this claim. We can say that this is when we know that he is sterile, or like BaHaG says, when they were together 10 years and he had children from another wife. We cannot give this answer here, for it would apply even if he is Yoreh k'Chetz!

Answer #1 (Rosh): Since he has children, we would not say that he did not merit to have children through her if not for her claim Eino Yoreh k'Chetz. When she claims, we suspect that he deteriorated after fathering his children. Since she waited 10 years, we are not concerned lest she seeks to marry another man.

Answer #2 (R. Shmuel, cited in Rosh): The case is, she waited 10 years with her third husband. This is like R. Shimon ben Gamliel, who says that three occurrences establish a Chazakah. Also the end of the Sugya says that three miscarriages make a Chazakah. This explains his claim that she is sterile. We cannot say that it is like Rebbi after 10 years with her second husband, for Rebbi agrees that he must pay a Kesuvah.