Gemara

(Rabah and Rav Yosef): Beis Shamai forbid Mi'un from Nisu'in because a person does not want to have Bi'as Zenus. (A man will not marry an orphan if she can do Mi'un and retroactively convert the Bi'os to Bi'as Zenus.)

Beis Hillel say, since there is Kidushin and a Kesuvah, people do not consider it to be Bi'as Zenus.

22a (Mishnah): A son from any mother exempts his father's wife from Yibum and Chalitzah. The only exceptions are a son from a slave or Nochris.

Kesuvos 72b (Rav): If a man was Mekadesh a girl on Tanai (conditionally) and did Nisu'in with her Stam (and the Tanai was not fulfilled), she needs a Get from him (before she can marry someone else);

(Shmuel): She does not need a Get.

(Abaye): Rav does not hold that since he did not mention the Tanai at the time of Nisu'in, this shows that he pardoned it. Rather, a man avoids Bi'as Zenus.

Question: Rav and Shmuel already argued about this elsewhere!

(Rav): If an orphaned minor (married mid'Rabanan) became an adult without doing Mi'un and married another man, she does not need a Get from the second man;

Shmuel: She needs a Get from the second man.

Answer: They needed to argue in both cases:

Had they argued only about a minor, one might have thought that there Rav does not require a Get because her first husband did not stipulate (therefore, he wants Bi'ah to make Kidushin mid'Oraisa once she matures). Rav would agree in our case, for the Mekadesh was insistent about his Tanai!

Had they argued only here, one might have thought that here Shmuel requires a Get because her first husband stipulated (he does not want Bi'ah to make Kidushin), but Shmuel would agree there, for there was no Tanai!

Gitin 81a (Mishnah - Beis Shamai): If a man divorced his wife and spent the night with her in an inn, he need not give her another Get;

Beis Hillel say, he must give her another Get.

This is when she was divorced from Nisu'in. If she was divorced from Eirusin, all agree that a second Get is not needed because he is not so intimate with her.

(Gemara - Rabah bar bar Chanah citing R. Yochanan): The argument is when witnesses saw that they had Bi'ah;

Beis Shamai hold that a man would have Bi'as Zenus. Beis Hillel hold that he would not (surely, he was Mekadesh her).

If witnesses did not see Bi'ah, no one requires a second Get.

If witnesses saw Bi'ah, it makes what difference whether the divorce was from Nisu'in or Eirusin! R. Yochanan holds like R. Shimon ben Elazar, who says that Beis Shamai and Beis Hillel argue about when witnesses saw Bi'ah. If not, no one requires a second Get.

Rishonim

Rif and Rosh (Yevamos 5a and 2:3): The Mishnah says that a child from a slave or Nochris does not exempt from Yibum and Chalitzah. Rabanan say that just like the Nochris is not his own, also the slave. However, if one had Bi'ah with his own slave, even though she does not have a Get Shichrur, the child is his. A man avoids Bi'as Zenus. (Surely, he freed her before Bi'ah.) If he has Bi'ah with her daughter, he is liable for Bi'ah with his own daughter. A Gaon was unsure about this. He is stringent about Isur to require Chalitzah. He is lenient about money; the slave's son does not inherit, but the heirs may not sell him. The son may not marry a Bas Yisrael without a Get Shichrur.

Rambam (Hilchos Gerushin 10:19): Some Ge'onim ruled that any woman who had Bi'ah in front of witnesses needs a Get. There is a Chazakah that a man avoids Bi'as Zenus. I say that this is very far from the ways of Hora'ah; one should not rely on it. Chachamim mentioned this Chazakah only regarding one's ex-wife, or one who was Mekadesh on Tanai and did Nisu'in Stam. With one's wife there is a Chazakah that a man avoids Bi'as Zenus unless he specifies that it is for Zenus or on condition. Regarding other women, every harlot is Muchzekes to have Bi'ah for Zenus unless he specified that it is l'Shem Kidushin.

Support (Magid Mishneh): The Rashba (Gitin 81b DH) supports this from Yevamos 97a, which permits a man to marry a woman raped or enticed by his father. We do not distinguish whether the Bi'ah was in front of one or two witnesses.

Rebuttal (Ra'avad): We follow the Ge'onim's words regarding Kosher people. They would not transgress Bi'as Zenus in front of witnesses. If he and she are immoral, we are not concerned for Kidushin.

Rosh (Gitin 8:13): Presumably, we say that he intended for Kidushin only when he had Bi'ah with his ex-wife from Eirusin, for then they regret the divorce. If unrelated people had Bi'ah, we are not concerned for Kidushin. R. Elazar says that if a Panuy and Penuyah (a single man and a single woman) had Bi'ah, she becomes a Zonah. He did not distinguish and say that if it was in front of witnesses the Bi'ah was l'Shem Kidushin.

Yam Shel Shlomo (Yevamos 2:10): In Yevamos (2:3), the Rosh agrees with R. Natrunai Ga'on that if a man had Bi'ah with his slave, whether it was like marriage or like Bi'as Zenus, surely he freed her beforehand. The Rosh does not apply the Chazakah that a man avoids Bi'as Zenus (because she was never married to him), rather, a person does not sin if he has a permitted way.

Teshuvas Rosh (32:13, cited in Tur Siman 26): If a Penuyah is living with a man, Beis Din forces him to expel her. Surely she is embarrassed to immerse, and he is Bo'el Nidah.

Rosh (35:10): The Chazakah that a man avoids Bi'as Zenus is not Vadai to obviate the need for a Get from someone else who was Mekadesh her afterwards. Rather, it creates Safek Kidushin.

Poskim

Shulchan Aruch (EH 26:1): A woman becomes an Eshes Ish only through proper Kidushin. Bi'as Zenus not l'Shem Kidushin, or even l'Shem Ishus without witnesses, is nothing, even if he designated her for himself. Just the contrary, we force him to expel her!

Gra (3): We find that Kidushin mid'Rabanan becomes mid'Oraisa when they are living together. Witnesses of seclusion are not required, because it is known that they have Bi'ah. Here is different, for we do not assume that they are l'Shem Kidushin.

Rema: If a Nochri married a Nochri, or a Meshumad (apostate) married a Meshumedes according to their creed and they converted, there is no concern for Kidushin. She can leave him without a Get. Even if she was with him several years, it was mere Zenus.

Gra (9): Here he surely has Bi'ah with intent for (no more than) the original 'Kidushin'.

Chelkas Mechokek (3): The Teshuvos indicate that we are not concerned for Kidushin because he does all Aveiros. This refers to people who willingly became apostates. Many of the Terumas ha'Deshen's reasons do not apply nowadays to people who are forced (to abandon Torah publicly) and observe Mitzvos privately. Many other Anusim know that they live together. One should not be lenient about Eshes Ish, especially if the couple is careful about Nidah.

Shulchan Aruch (33:1): Some say that if a Panuy and Penuyah had Bi'ah in front of witnesses, we are concerned lest he intended for Kidushin, for there is a Chazakah that a man avoids Bi'as Zenus. If he was Muchzak to have Zenus or he has a wife, we are not concerned. Some are lenient in every case.

Darchei Moshe: The Tur connotes that if they were not discussing Kidushin, she is not Mekudeshes. The Mordechai (Kidushin 533) requires a Get. If she later had Bi'ah with another man, she needs a Get also from him. (The Mordechai and Hagahos Ashri (Kidushin 4:4) cite this in the name of R. Baruch.)

Shulchan Aruch (149:5): The Chazakah that a man avoids Bi'as Zenus applies only to one's ex-wife, or one who was Mekadesh on Tanai and had Bi'ah Stam. With one's wife there is a Chazakah that a man avoids Bi'as Zenus unless he specifies that it is for Zenus or on condition. Regarding other women, the Chazakah is that Bi'ah is for Zenus unless he specified that it is l'Shem Kidushin.

Shulchan Aruch (6): Similarly, if a man and his wife became Meshumadim due to royal decrees and married each other according to Nochri law, even though it is know that they are secluded every day, we are not concerned for Kidushin.

Source (Rivash 6): A case occurred in which two Anusim married each other according to Nochri law and lived together; she became pregnant. Even regarding seclusion with one's ex-wife. The Rashba adds that we are concerned only if they saw the witnesses, for a person knows that Kidushin without witnesses is invalid. Therefore, if he did not know about the witnesses he did not intend for Kidushin. The Tosefta (Kidushin 1:1) says that Bi'ah makes Kidushin only if it is l'Shem Kidushin, i.e. explicitly l'Shem Kidushin. Therefore, we are not concerned in this case.

Suggestion: Perhaps even the Rambam would be concerned when they wanted to be married! This is no worse than discussing Kidushin!

Rejection (Rivash): Even the Ge'onim who are concerned about a Panuy and Penuyah would not be concerned here. Since they were married like Nochrim, they showed that they do not want Torah Kidushin. She is like a Pilegesh (concubine) without Kidushin or Kesuvah. In our case there was no Mikveh in the area. They were not concerned for Safek Kares (when a woman is asked to go to Chupah, she must count seven clean days and immerse lest she saw Dam Nidah due to desire). All the more so they are not concerned for the Isur of a Penuyah! The Ro'oh does not require witnesses of seclusion when a Ketanah married mid'Rabanan grows up because everyone knows that they are having Bi'ah, but all the Rishonim disagree. We do not seek stringencies to make a woman an Agunah.

Mishneh l'Melech: The Rivash did not say that he does not intend for Kidushin because he relies on the (Nochri) marriage ceremony he did. This is because we say that a person relies on his previous Kidushin regarding nuptial gifts, but not regarding Bi'ah.