Who is a mamzer? [The child of] any blood relation with whom cohabitation is prohibited by a negative commandment; [these are] the words of R' Akiva. Shimon HaTimni says: [The child of] anyone for whom the punishment is kares at the hands of heaven, and the halachah follows his view. R' Yehoshua says: [The child of] anyone for whom the punishment is death at the hands of the court. R' Shimon ben Azzai said: I found a genealogical scroll in Jerusalem, in which was written —- “So-and-so is a mamzer from a married woman,” supporting R' Yehoshua's words.  One whose wife died is permitted to [marry] her sister. [If] he divorced her and she died, he is permitted to [marry] her sister. [If] she married someone else and she died, he is permitted to [marry] her sister. [If] his yevamah died, he is permitted to [marry] her sister. [If] he performed chalitzah with her and she died, he is permitted to [marry] her sister.

Rabban Gamliel says: There is no [validity to] a bill of divorce after a bill of divorce, nor [to] maamar after maamar, nor [to] cohabitation after cohabitation, nor [to] chalitzah after chalitzah. The Sages [however] say: There is [validity to] a bill of divorce after a bill of divorce, and [to] maamar after maamar; but after cohabitation or after chalitzah there is nothing.