DO WE ASSUME THAT BI'AH WAS FOR KIDUSHIN? [Ein Adam Oseh Be'ilaso Bi'as Zenus]
Gemara
Question: If there were three Kodesh animals, i.e. two Tamim and a Ba'al Mum, and three Chulin Tamim, and he said "Elu Tachas Elu," what is the law?
Since for the majority of these three transactions (the Tamim), "Tachas" (perforce) makes Temurah, also for the third;
Or, even here, one does not sin (regarding the Hekdesh Ba'al Mum) unless he must! (He intends to redeem the Ba'al Mum.)
Kesuvos 72b (Rav): If a man was Mekadesh a girl on Tanai (e.g. on condition that she has no vows or Mumim) 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 infer that since he did not mention the Tanai at the time of Nisu'in, he pardoned it. Rather, Ein Adam Oseh Be'ilaso Bi'as Zenus (a man does not have extramarital relations).
Kidushin 10a - Question: Does the beginning of Bi'ah acquire, or the end?
This affects a woman who received Kidushin money from Shimon while having Bi'as Kidushin with Reuven, or a Kohen Gadol who is Mekadesh a virgin with Bi'ah. (If he acquires only at the end of Bi'ah, she is no longer a virgin, and she is forbidden to him.)
Answer (Ameimar): Anyone who has Bi'ah intends for a full act of Bi'ah.
Rishonim
Rambam (Hilchos Temurah 2:3): If there were three Korbanos, one of which had a Mum, and three Chulin Tamim, and he said "Elu Tachas Elu," two Chulin animals become Temurah for the Tamim, and he is lashed twice for this. The third is a redemption of the Ba'al Mum. Since he can be Mekadesh the third through Isur (Temurah) or Heter (redemption), one does not abandon Heter to do Isur.
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 does not have Bi'as Zenus. I say that 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 for Kidushin.
Support (Magid Mishneh): The Rashba (Gitin 81b DH Nisgarshah) 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 bachelor and Penuyah (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.
Teshuvas Rosh (35:10): The Chazakah that a man avoids Bi'as Zenus is not Vadai to exempt from a Get from someone else who was Mekadesh her afterwards. Rather, it creates Safek Kidushin.
Rashba (Teshuvos Chadashos 162, brought in Beis Yosef EH 17): Rachel came to a city and said that she is single. She became Mekudeshes to Shimon for a Pilegesh (concubine), i.e. Kidushin without a Kesuvah, and lived with him for several days and was secluded with him. Later it became known that Reuven was Mekadesh her years earlier. Afterwards, her sister brought to her a Get (not validated) from Reuven dated after Shimon's Kidushin. Surely she needs a Get from both of them, just like a woman who heard that her husband died and remarried, and her husband came. (Perhaps people will say that Reuven divorced her and Shimon was Mekadesh her, and she leaves him without a Get.) Further, here she needs a Get from Shimon due to Safek. Since Shimon heard about Reuven's Kidushin, and he saw her Get, he knows that his Kidushin was invalid, so afterwards he had Bi'ah with her for Kidushin. Rav holds that when a man is Mekadesh a minor, he knows that his Kidushin was invalid (mid'Oraisa), so when they have Bi'ah after she matures, he intends for Kidushin (mid'Oraisa). Even though here Shimon was forbidden to her (due to adultery before the Get), Kidushin takes effect on her.
Shiltei ha'Giborim (Gitin Sof 35a): If a woman was divorced from Nisu'in, and remarried and was widowed, and then was secluded with her ex-husband, she does not need a Get from him, even if they had Bi'ah. The Bi'ah was for Zenus, and not for Kidushin. If it was for Kidushin, he would be lashed for Machazir Gerushaso (remarrying his divorcee)!
Mordechai (Kidushin 533): If a bachelor had Bi'ah with a Penuyah, and witnesses saw from the outside, she needs a Get. If another man had Bi'ah with her afterwards, she needs a Get also from him. The Rambam disagrees.
Poskim and Acharonim
Shulchan Aruch (EH 33:1): Some say that if a bachelor and Penuyah had Bi'ah in front of witnesses, we are concerned lest he intended for Kidushin, for there is a Chazakah that Ein Adam Oseh.... 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 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.)
Chelkas Mechokek (5): Above (Rema 27:3), we said about Kidushei Kesef that if he intended for Kidushin, even if he gave to her silently, it is Kidushin. (If so, why do we say here that it is due to the Chazakah? - Machatzis ha'Shekel) We must say that here, even if he says that he did not intend for Kidushin, he is not believed against the Chazakah that Ein Adam Oseh....
Beis Shmuel (5): I wrote above (27:12) that even if both intended for Kidushin, if they did not explicitly say that he is Mekadesh her, it is not Kidushin. Here, according to the opinion that Ein Adam Oseh..., it is as if he said this.
Mishneh l'Melech (10:18): The Radvaz (1:351) wrote that if she turned Nidah and a man was secluded with her, we are not concerned for Bi'ah. Even if we know that they had Bi'ah, we are not concerned for Kidushin. We cannot say Ein Adam Oseh Be'ilaso Bi'as Zenus, for one who is not concerned for the Isur Kares for Nidah is not concerned for Bi'as Zenus. I agree, and even if we are unsure whether or not he knew that she is Nidah. Presumably she told him, and he was not concerned. Also, the Chazakah Ein Adam Oseh Be'ilaso Bi'as Zenus was said regarding both of them.
Magihah: Also Bnei Chayei (38) and Leket ha'Kemach (90) agreed that the Chazakah applies to both of them, unlike Pnei Moshe 1:62. However, Leket ha'Kemach (189) retracted and proved from the Radvaz that the Chazakah applies only to the man.
Chidushei ha'Rim (Kesuvos 73a): If the Chazakah that Adam Oseh... did not apply also to the woman, there would be no source that she consents to the Kidushin!
Mishneh l'Melech: Kidushin requires her consent. Since she is not concerned for the Isur Nidah, all the more so she is not concerned for Bi'as Zenus. The Rambam wrote that even when we know that a man transgressed Temurah on two animals, if it is possible that he did Temurah on the third, or redeemed it b'Heter, we assume that he minimized Isurim. There is different, for they are separate. Here, in one Bi'ah he transgressed Nidah. Surely he was not careful about another Isur (Zenus) in the Bi'ah itself.
Avnei Milu'im (1): This is unlike the Rashba, who says that even though Shimon was forbidden to her, he has Bi'ah for Kidushin. Shiltei ha'Giborim connotes like the Radvaz. However, it seems that in the Radvaz' case, Shiltei ha'Giborim would say that he has Bi'ah for Kidushin. Even though he did an Isur, the Chazakah Ein Adam Oseh Be'ilaso Bi'as Zenus remains. Regarding Machazir Gerushaso, one is lashed only if he was Mekadesh her, but not for Bi'ah without Kidushin. Presumably he intends for the smaller Isur. The Isur of Nidah does not depend on Kidushin, so the Chazakah that Ein Adam Oseh... remains. One suspected about one matter is not suspected about other matters. Only regarding people who wantonly have Zenus, there is no Chazakah. Shiltei ha'Giborim did not say that since he transgresses in any case, there is no Chazakah. The Rashba must hold that the Isur Aseh of an adultress to the Bo'el does not depend on whether or not he was Mekadesh her. This requires investigation.
Avnei Milu'im (DH v'Hinei): In Kesuvos 73a, Rashi explained that a man pardons the Tanai because Ein Adam Oseh..., but he does not pardon it regarding Kesuvah. Shitah Mekubetzes asked that if she has a vow (or Mum) and he can divorce her without paying a Kesuvah, it is Bi'as Zenus! He answered that since he stipulated about vows and she accepted, he assumes that she has no vows. (It is not light in his eyes to divorce her, for he assumes that he would need to pay a Kesuvah.) He is merely stringent to pardon the Tanai regarding Kidushin, in case she has vows. If it is Kidushin because the Chazakah applies to both of them, when she knows that she has vows (and she has no Kesuvah), in any case it is Bi'as Zenus, so what is the source that she intends for Kidushin? This is not difficult for the Ran (33b), who says that he pardons the Tanai and retroactively, the Kidushin money made Kidushin.
Note: She is sure that now he does not know about the vow or Mum, so at the time of this Bi'ah it is not light in his eyes to divorce her. Perhaps she intends for Kidushin to avoid Bi'as Zenus in this Bi'ah! Indeed, once he learns about them and knows that he can divorce her for free, any future Bi'ah is Bi'as Zenus!
Chidushei ha'Rim (Kidushin 10a DH Kol): What is the source that a man intends for Sof Bi'ah? I answer that even if he intended for the beginning, since it is a Safek, he does not acquire at the start, for it is as if there are no witnesses (since it is a Safek whether he intends now for Kidushin). However, if so, why does he acquire at the end? Perhaps he intended to acquire only at the beginning! (He does not intend to acquire through Sof Bi'ah, for he assumes that he already acquired.) I answer that because Ein Adam Oseh..., he is concerned lest he not acquire at the beginning, and intends to acquire through Sof Bi'ah.
Chidushei ha'Rim (DH Oh): We should say that because Ein Adam Oseh..., he surely intends to acquire from the beginning, to avoid the Isur of Bi'as Zenus! I answer that there is no Bi'as Zenus, for the Kidushin begins at the start of Bi'ah and finishes at the end.