One says to a woman: I married you. And she says: I you did not marry me. It is prohibited for him to come close to her and she is allowed to come close to him.
[She says:] You married me, and he says: I did not marry you. He is allowed in coming close to her and she is prohibited in coming close to him.
I married you, and she says: you did not marry [me], rather [you married] my daughter. He is prohibited in coming close to the mother, and the mother is allowed in coming close to him; and he is allowed in coming close to the daughter, and the daughter is allowed in coming close to him.
[One says:] I married your daughter. And she (the mother) says: you did not marry [her], rather you married me. He is prohibited in coming close to the daughter, and the daughter is allowed in coming close to him; and he is allowed in coming close to the mother, and the mother is prohibited regarding coming close to him.
All of these that claim marriage, are like the claim of a one who claims that there are witnesses there [at the scene of something], and they (judges) went to them (the witnesses) and to the state afterwards or they (the witnesses) died. But, if they rejoice that they were married [and there were not] two witnesses, there is not marriage here.
Any time that a woman says to a man, "you married me" and he says, "I did not marry you," we ask him to write for her a bill of divorce. Rem"a: And at this point he is forbidden to her relatives, since he gave her a bill of divorce. However, if he said, "I married you" and she says, "you did not marry me" and we coerce him to give her a bill of divorce because we are concerned that other men will not marry her [because of a concern that she is a married woman], [in such an instance,] the woman is not forbidden to his relatives because of the bill of divorce (source: Commentary of Mordechai on Masechet Kidushin)
Someone who says: Before I married my wife, I married her sister in front of "so and so," and they have since moved to another town, I never gave her a divorce, and she is now married. He is not believed to prohibit her from living with her husband, as long as witnesses are not brought (to prove otherwise). And even if she says: It is true that he married me, she is still not believed to prohibit herself from her husband, even if witnesses are brought that he married her. If his wife's sister was married in front of him, she is not prohibited from her husband, for this is prohibited with his wife, since it is says: he married her sister first, then he is prohibited from both family members.