Gemara

(Abaye): Kidushin she'Ein Mesurin l'Vi'ah (this will be explained) is Kidushin;

(Rava): It is not Kidushin.

(Bar Ahina): "When a man will take (be Mekadesh) a woman and have Bi'ah with her" - Kidushin must be fit for Bi'ah.

(Mishnah): If a man was Mekadesh at once a woman and her daughter, or two sisters, they are not Mekudashos.

Inference: If he was Mekadesh one of the two women (Stam, without specifying which), one is Mekudeshes.

Question (against Rava): Even though Bi'ah is forbidden, for it is a Safek which is Mekudeshes (each woman could be his wife's relative), the Kidushin works!

Counter-question (Rava - Seifa): A case occurred in which one was Mekadesh five women, two of whom were sisters... Chachamim ruled that the sisters are not Mekudashos (but the unrelated women are Mekudashos).

Had he said 'all of you are Mekudashos to me', since both sisters cannot become Mekudashos, also the others would not, just like 'you and the donkey should acquire', does not work. Rather, he said 'one of you is Mekudeshes to me', and the Mishnah says that neither sister is (even Safek) Mekudeshes!

Question: The Reisha is unlike Rava, and the Seifa is unlike Abaye!

Answer #1 (for Abaye): If one was Mekadesh two sisters at once, they are not Mekudashos. If he was Mekadesh one Stam, one is Mekudeshes;

If he said 'I am Mekadesh whichever of you may have Bi'ah with me', neither is Mekudeshes. Such a case occurred with five women... Chachamim ruled that the sisters are not Mekudashos.

Answer #2 (for Rava): If one was Mekadesh two sisters Stam, it is as if he was Mekadesh both at once. Neither is Mekudeshes;

A case occurred involving five women... he was Mekadesh 'all of you, and one of the sisters.' Chachamim ruled that the sisters are not Mekudashos.

(Mishnah): If Levi was Mekadesh his daughter to David, without specifying which daughter, the Bogros (adult daughters) are not even doubtfully Mekudashos.

Question (against Rava): This implies that the minors (and Na'aros) are (Safek) Mekudashos, even though the Kidushin forbids Bi'ah!

Answer: The case is, Levi has only one Bogeres (who made him a Shali'ach to be Mekadesh her) and one minor. The Mishnah teaches that we are not concerned lest he accepted Kidushin for the Bogeres. Rather, he accepted for the minor, for that is a Mitzvah incumbent on him, and he keeps the money.

52a - Question (Tivyomi's Beraisa): Reuven has five sons and David has five daughters. If Reuven was Mekadesh 'one of your daughters to one of my sons', each daughter needs a Get from each son.

Rava is refuted.

Yevamos 23b (Mishnah): If one was Mekadesh one of two sisters and does not know which, he divorces both.

Suggestion: This teaches that Kidushin she'Ein Mesurin l'Vi'ah takes effect!

Rejection: No. At the time of Kidushin, he knew which he was Mekadesh. Later, he became unsure. This is why the Mishnah says 'he does not know', not 'it is not known'. The Chidush is the Seifa (if he died and left two brothers, one may not do Yibum until the other does Chalitzah, lest he has Bi'ah with his Yevamah's sister.

Rishonim

Rif: Abaye and Rava argue about Kidushin she'Ein Mesurin l'Vi'ah, e.g. Reuven said to Levi 'one of your daughters is Mekudeshes to me with this Perutah'. This is one of the places in which the Halachah follows Abaye against Rava. Therefore, all of his daughters need a Get.

Rif and Rosh (Yevamos 5a and 2:4): We tried to prove from our Mishnah that Kidushin she'Ein Mesurin l'Vi'ah is Kidushin, and showed how Rava could answer. Since the Halachah follows Abaye, our Mishnah can be understood simply. Even if it was never known whom he was Mekadesh, each needs a Get.

Rambam (Hilchos Ishus 9:3): If Reuven said to two sisters 'one of you is Mekudeshes to me' and he gave to them a Perutah, or one received on behalf of her sister, or if he said to Levi 'one of your daughters is Mekudeshes to me', they all need a Get. Even though Bi'ah is forbidden, Kidushin Chachamim.

Tosfos (51a DH Kidushin): Kidushin she'Ein Mesurin l'Vi'ah is when the Kidushin itself forbids Bi'ah with her. Kidushin with Chayavei Lavin is considered Mesurin l'Vi'ah (Rava agrees that it takes effect).

Or Zaru'a (Hilchos Yibum 602): Kidushin of a Nefel (stillborn baby) does not take effect. Even though we say that Kidushin she'Ein Mesurin l'Vi'ah are Kidushin, this applies to one who will live and be fitting for marriage.

Poskim

Shulchan Aruch (EH 41:2): If one was Mekadesh at once two women such that he cannot be married to both due to Ervah, e.g. two sisters, neither is Mekudeshes. No one needs a Get. If he was Mekadesh one Stam, e.g. he said to Levi 'one of your daughters is Mekudeshes to me', or if a woman was a Shali'ach to accept Kidushin for her sister(s) and he said 'one of you is Mekudeshes to me', they all need a Get. Bi'ah with any one is forbidden, lest she is Achos Ishto.

Acharonim

Question (Mishneh l'Melech Hilchos Ishus 7:20 DH Od Nistapakti): The Rambam (7:2) says that if one made a Shali'ach to Mekadesh a woman and he was Mekadesh conditionally, it is invalid. Why does Kidushin she'Ein Mesurin l'Vi'ah work through a Shali'ach? The Mekadesh is forbidden to all the women and must divorce them. Surely he did not appoint a Shali'ach for this! However, Tivyomi's Beraisa shows that the Kidushin works! This requires investigation.

Answer (Magihah to Mishneh l'Melech): We can similarly ask about one who was a Shali'ach to be Mekadesh his Bogeres, and he was Mekadesh 'my daughter' Stam. We say that the Bogeres is not Mekudeshes, for a man prefers to be Mekadesh his Ketanah; he keeps the money, and it is a Mitzvah incumbent on him. We did not say that one does not make a Shali'ach for Kidushin she'Ein Mesurin l'Vi'ah! Normally, one is not so brazen to make his or her father a Shali'ach. Perhaps one who does so accepts whatever the father does. The RaMaH (cited in Tur, middle of Siman 35) supports this. (If Yakov told his son Levi that he wants to Mekadesh Levi to Plonis, Levi was silent, and Yakov did so, it is Vadai Kidushin. Levi was embarrassed to refuse, so he made his father a Shali'ach. If anyone else said and did so, it would be Safek Kidushin.)

Note: Perhaps Tivyomi's Beraisa discusses sons who explicitly made their father a Shali'ach for any Kidushin. The Beraisa teaches about Kidushin she'Ein Mesurin l'Vi'ah; it did not elaborate to explain why the Shelichus is valid. However, the Rambam, Shulchan Aruch and others discuss Kidushin she'Ein Mesurin l'Vi'ah through a Shali'ach other than a father, without mentioning this stipulation. Elsewhere, if one was ashamed to say that he objects, the Shelichus is invalid (Bava Metzi'a 22a). I have no source that it is brazen for a girl to make her father a Shali'ach to be Mekadesh her.