Gemara

91a (Mishnah): If she remarried without permission of Beis Din, she may return to her husband).

(Rav Huna citing Rav): This is the Halachah.

Objection (Rav Nachman): Why do you speak deceptively (as if all agree to this)?! If you hold like R. Shimon, say that the Halachah follows R. Shimon!

Question #1 (Rav Sheshes): 'This is the Halachah' implies that others argue (and forbid her to the first husband). What did she do wrong (that she should be fined)?!

Question #2 (Rav Sheshes): A Beraisa proves that Chachamim agree with R. Shimon!

(Beraisa): All Arayos (who married) do not require a Get, except for an Eshes Ish who remarried according to Beis Din (i.e. one witness).

Inference: If she remarried according to two witnesses, no Get is needed.

Answer #1 (to Question #2): The Beraisa is like R. Shimon.

Answer #2: Really, the Beraisa is Chachamim. It means that Arayos do not require a Get, except for a married woman who remarried based on (two witnesses or) a ruling of Beis Din.

91b: Rav Papa was about to permit a woman to return to her husband, because she was blameless.

Objection (Rav Huna brei d'Rav Yehoshua): We brought many Mishnayos showing that we fine her anyway!

Answer (Rav Papa): We answered that in all of them, she was to blame!

Objection (Rav Huna): Will we rely on those answers?!

95a (Mishnah - R. Yosi): Anyone who forbids others forbids to himself. Anyone who does not forbid others does not forbid to himself (this will be explained).

The first Tana said that if Reuven's wife Leah and Giso (David, the husband of Leah's sister Rachel) went overseas (and we heard that they died, and Reuven married Rachel), David's wife becomes forbidden to David, and Reuven's wife is permitted (to Reuven). R. Yosi says, just like his David's wife is forbidden, also Reuven's wife is forbidden.

Question: How do we explain 'anyone who does not forbid to others does not forbid to himself'?

Answer #1 (R. Ami): This refers to the Reisha (87b). If a woman remarried according to Beis Din or based on (two) witnesses, she must leave her husband;

Here, the first Tana says, whether Reuven married Achos Ishto based on witnesses and she remains permitted to her husband, or he married her according to Beis Din and she is forbidden to her husband, Reuven remains permitted to his wife;

R. Yosi says, when he married her according to Beis Din he forbids others, and he also forbids his own wife on himself. When he married based on witnesses he does not forbid others, and he does not forbid to himself.

Answer #2 (R. Yitzchak Nafcha): It refers to the Seifa (94a). R. Yosi distinguishes between when Leah was Mekudeshes to Reuven and when she was Nesu'ah;

The first Tana says, whether there was Kidushin or Nisu'in, Rachel is forbidden (to David) and Leah is permitted to Reuven;

R. Yosi says, if there was Nisu'in, we are not concerned lest people say that Leah's Nisu'in was on condition. (It is clear that the marriage to Rachel was a mistake, so) he does not forbid to others (people will not say that Rachel was divorced, married Reuven, and now remarries David), and he does not forbid his wife to himself;

If there was Kidushin, we are concerned lest people say that Leah's Kidushin was on condition (and it was not fulfilled, and Reuven truly married her after David divorced her), he forbids to others (David), he even forbids to himself (Leah looks like Achos Gerushaso).

(Rav Yehudah citing Shmuel): The Halachah follows R. Yosi.

Objection (Rav Yosef): Elsewhere, Shmuel taught differently!

(Rav): A Yevamah is like an Eshes Ish;

(Shmuel): She is not like an Eshes Ish.

(Rav Huna): The case is, Reuven was Mekadesh a woman and went overseas. Reuven's brother heard that Reuven died, and married her. Rav says that she is like an Eshes Ish, and she is forbidden to Reuven. Shmuel says that she is not like an Eshes Ish, and is permitted to Reuven.

Answer #1 (Abaye): Shmuel ruled like R. Yosi, but he did not say that this is like R. Yitzchak Nafcha explains the argument. Perhaps he explains like R. Ami!

Answer #2 (Abaye): Even if he explains like R. Yitzchak, perhaps he rules like R. Yosi regarding 'anyone who does not forbid', but not regarding 'anyone who forbids'!

Answers #3,4 (Abaye): Perhaps Rav and Shmuel do not argue like Rav Huna explained. Rather, they argue about Rav Hamnuna's law (that Bi'as Zenus forbids a Yevamah to her Yavam), or whether or not Kidushin of a stranger takes effect on a Yevamah.

Rishonim

Rif (27b) and Rosh (10:1): The Gemara says that she must leave both men in the Reisha, when she married based on one witness. In the Seifa, when she got married without permission, rather, according to two witnesses, she may return to her husband, for she was Anusah. What could she have done?! Also Rav taught that when she remarried based on two witnesses she does not leave her initial Heter to her first husband. This is not the Halachah. Rather, whether she remarried based on one or two witnesses she must leave both men, and all the fines apply. Rav Papa was about to permit a woman because she was blameless, and Rav Huna brei d'Rav Yehoshua convinced him not to. This shows that the Halachah does not follow Rav and R. Shimon.

Ba'al ha'Ma'or (30b): Shmuel taught that the Halachah follows R. Yosi in the Mishnah (94b). The Gemara did not resolve how Shmuel understands the Mishnah! Whether we explain like R. Ami or R. Yitzchak Nafcha, R. Yosi holds like R. Shimon (who says that she returns to her husband if she married according to witnesses).

The Rif says that Rav Papa wanted to permit a woman who remarried according to two witnesses. Rav Huna convinced him not to, i.e. l'Chatchilah. If she transgressed and returned to her first husband, she need not leave and her children are not Mamzerim. Rav and Shmuel permit her to return, surely we rely on them b'Di'eved! Alternatively, the Halachah follows them l'Chatchilah. Rav Papa did not intend to permit one who remarried based on two witnesses, for Rav and Shmuel explicitly permitted this! Rather, they permitted a case like the Mishnayos brought. E.g. a Yevamah married l'Shuk after her Tzarah did Yibum and she heard that the Tzarah became pregnant, and this was false and the Tzarah was found to be an Ailonis. Alternatively, a divorcee showed her Get to someone who erred and told her that it is Kosher. Even though in the Mishnayos she is forbidden, Rav Papa thought that she is permitted because she did wait or show her Get to someone. Rav Huna replied that we should not rely on the answers, for the Mishnayos, read simply, say that she is fined in any case. Chachamim made a uniform decree.

Rebuttal (Milchamos Hash-m): There is no proof according to R. Yitzchak Nafcha that R. Yosi argues with R. Shimon! Therefore, we do not abandon what Basrai ruled, that we do not permit a woman who was Anusah. Also R. Akiva forbids Achos Ishto, even though the case arises only through two witnesses. (We believe one witness about an Eshes Ish to enable her to remarry. There is no reason to be lenient to let her marry her sister's husband without proper testimony that her sister died.) People are more likely to think that an Eshes Ish remarried after receiving a Get than to suspect that one was able to marry Achos Ishto because his Kidushin was on condition; this is why Chachamim permit Achos Ishto. The Halachah follows R. Akiva; all the more so, we are stringent about Eshes Ish who remarried based on two witnesses. The only Tana who explicitly permits is R. Shimon. The Gemara says that we do not rely on the (weak) answers for the Mishnayos. Even if Rav and Shmuel hold like R. Shimon, we rule like Basrai.

Rambam (Hilchos Gerushin 10:5): If witnesses told a woman that her husband died and she remarried and her husband returned, whether her original and new husbands are healthy or Chereshim who cannot Mekadesh fully, she must leave both men and is forbidden to them forever.

Poskim

Shulchan Aruch (EH 17:56): If a man went overseas and they told his wife that he died, and she remarried and her husband returned, whether she married according to one or two witnesses, she must leave both men (Rema - even if she did not have Bi'ah with the latter). She needs a Get from both...

Beis Shmuel (161): Even if she was secluded with her new husband after Kidushin (without Bi'ah), the fines apply.

Yam Shel Shlomo (10:3): Only the Ba'al ha'Ma'or permits one who remarried based on two witnesses. Even though the Reisha (87b) discusses one who remarried based on one witness, it says 'they told her' to teach that it also applies when two witnesses told her. Even though the Nimukei Yosef proved that sometimes 'Amru' refers to one witness, when we can explain that it means two, we do.