Yevamos, Chapter 4, Mishnah 13. This Mishnah expands on the ideas raised in the previous Mishnah regarding who is a mamzer, and continues to discuss the prohibition of marrying one's wife's sister.
"Eizehu mamzer?" - who is a mamzer? Three opinions:
Rabbi Akiva: "Kol she'ar basar shehu b'lo yavo" - any relative to whom a negative prohibition applies, whom one is forbidden to marry.
Shimon HaTimni: "Kol shechayavin alav kareis bidei Shamayim" - only a union that carries liability for kareis produces a mamzer.
Rabbi Yehoshua: "Kol shechayavin alav misah bidei beis din" - only a union punishable by death produces a mamzer, and this includes that it also carries liability for kareis.
There is a difference of opinion as to how to read Rabbi Akiva's words: does he mean that there must be a blood relative whose marriage carries a negative prohibition? The Rambam explains that the words are to be read as "kol she'ar basar, veshehu b'lo yavo" - that is, a family relative, and likewise anyone whose union carries a negative prohibition. This reading is reasonable, since the previous Mishnah listed even one who remarries his divorcee, and although she was his wife at a certain stage, she is not a blood relative in the plain sense. From here we have proof that Rabbi Akiva holds that even ordinary cases of negative prohibitions, and couples whose union carries a prohibition, produce a mamzer, even though their prohibition is not based on family relationship.
Concerning the words of Shimon HaTimni the Mishnah states: "Vehalachah kidvarav" - and the halachah follows his words. And indeed the halachah is decided in accordance with Shimon HaTimni, but we do not rule this way because the Mishnah says "the halachah follows his words," for we do not decide halachah on the basis of the Mishnah even when it itself renders a decision, but rather on the basis of the Gemara's ruling.
The testimony of Ben Azzai:
Rabbi Shimon ben Azzai relates an incident that occurred: "Matzasi megillas yuchsin biYerushalayim, vechasuv bah: ish peloni mamzer me'eishes ish" - I found a scroll of lineage in Jerusalem, and written in it was: so-and-so is a mamzer from a married woman. In that scroll, a halachic document dealing with matters of lineage, it was written about a certain man that he was a mamzer, because he came from an adulterous union: his mother was a married woman, wed to one man, who had relations with another, and he was the product of that union - and for this reason he was a mamzer. The Mishnah concludes: this document is "lekayem divrei Rabbi Yehoshua" - to uphold the words of Rabbi Yehoshua, since it supports his position that a mamzer comes only from unions punishable by death.
And where does the proof lie? For if this were not so, why would the scroll of lineage take the trouble to specify that he came from this particular type of union? Rather, it came to teach this halachah, that it must be the sort of forbidden union whose penalty is death at the hands of beis din.
One's wife's sister:
From here the Mishnah moves to the prohibition of one's wife's sister, which applies only during the wife's lifetime, and it lists several versions of the sister becoming permitted after the wife's death. It is worth noting that, as the Gemara points out, not all of the cases are necessary: at times the Mishnah lays out various scenarios even though the halachah is already clear from the first case.
"Ishto shemeisah - mutar ba'achosah" - if his wife died, he is permitted to her sister. This is the straightforward law.
"Gireshah umeisah" - he divorced his wife and afterward she died; he is permitted to her sister. And there is no reason to think otherwise, since the divorce did not change the fact that she died.
"Nisses le'acher umeisah" - after she was divorced she married another man and then died, and in this case too he is permitted to her sister.
"Yevimto shemeisah" - his brother died without children, and he has a bond with the widow, and therefore he cannot marry her sister; once she died, he is permitted to her sister. And here there was no marriage at all, only a bond, and according to most understandings the prohibition of her relatives is only rabbinic.
"Chalatz livimto umeisah" - he performed chalitzah with his yevamah and afterward she died; he is permitted to her sister. For the sister of the woman with whom he performed chalitzah is forbidden only rabbinically, because she resembles the sister of his divorcee, and once she died there is no problem here.
In summary: in this Mishnah the Tannaim disagree about the definition of a mamzer - from a blood relative and from unions carrying a negative prohibition (Rabbi Akiva), from unions carrying kareis (Shimon HaTimni), or from unions punishable by death at the hands of beis din (Rabbi Yehoshua) - and Ben Azzai brought proof for Rabbi Yehoshua's words from a scroll of lineage. We then learned that the prohibition of one's wife's sister applies only during her lifetime, and in all the scenarios the Mishnah listed - divorce, marriage to another, the bond of yibum and chalitzah - the sister is permitted once the woman has died.