Gemara

(Beraisa): (A Ken is a pair of birds. One will be offered for a Chatas, and the other for an Olah. Oleh v'Yored is a Korban for which rich people bring animals, and an Oni brings birds.) If one who must bring a Ken (for Oleh v'Yored) designated money for it (and then became rich), he may use all the money for Chatas Behemah (an animal) if he wants, or all for Olas Behemah;

If he died, leaving Stam money (he did not specify how much is for each Korban), it goes to Nedavah.

26b (Rav Chisda): A Ken becomes Mefurash (specified, which bird is the Chatas and which is the Olah) only when the owner buys it, or when the Kohen offers it.

Kerisus 28a (Rav Simi bar Ashi): Rav Chisda learns from "v'Lokchah Shtei Sorim..." and "v'Osah ha'Kohen..." (both verses say that one is for Chatas, and one is for Olah). The owner decides which is for which at the time of purchase, or the Kohen decides at the time of Hakravah.

Question (Beraisa): "V'Osahu Chatas" - the Goral (lottery) fixes one of the two goats of Yom Kipur to be a Chatas, but Shem (calling it a Chatas) does not.

Suggestion: Shem causes a bird to be a Chatas, but Goral does not. Goral causes a goat to be a Chatas, all the more so Shem should work!

Rejection: The verse teaches that this is not so.

Summation of question: Presumably, the case of Shem is like that of Goral. It is not at the time of purchase nor at the time of Hakravah!

Answer (Rava): The Beraisa means that Goral does not work for birds even at the time of purchase or Hakravah, but Shem works at these times. Goral works for goats not at the time of purchase or Hakravah, all the more so Shem should work at these times! The verse refutes this.

Question (Beraisa): If an Oni transgressed Tum'as Mikdash, and was Makdish money for a Kan, and became rich, and (later - Shitah deletes this) said, "these coins are for my Chatas (ha'Of), and these are for my Olah," he adds to the Chatas money to buy an animal. He may not use the Olah money.

Here, his Perush was not at the time of Hekdesh or Hakravah, and he may use only the Chatas money. (This shows that his Perush took effect!)

Objection (Rav Sheshes): The Beraisa is mistaken. It says (or implies) that he was Mefaresh after he became rich, but R. Elazar taught that if an Ashir brought Korban Oni for Tum'as Mikdash, he was not Yotzei (so surely, an Ashir cannot be Mefaresh)! Rather, the Beraisa should say that he was Mefaresh while he was still poor.

Answer #1 (Rav Sheshes): (Since in any case we must fix the Beraisa,) we fix it to say that he was Mefaresh at the time of Hekdesh.

Question: R. Chana said that an if Ashir brought a Korban Oni for Tum'as Mikdash, he was Yotzei (just like our text of the Beraisa). How can he answer?

Answer #2 (text of Bach): Instead of "(he was Makdish, became rich,) and then said...", it should say "(he became rich,) and later was Makdish and said...."

Yoma 41b - Question: The Beraisa says that he adds to the Chatas to buy an animal, i.e. he redeems it. Birds cannot be redeemed!

Answer (Rav Papa): The case is, he bought one bird. If he bought the Olah, he adds to the Chatas money to buy an animal, and the Olah will be a Nedavah. If he bought the Chatas, he cannot use the Olah money for Chatas Behemah.

Eruvin 37a (Mishnah - R. Yosi): If each of two women are obligated to offer a Ken (Chatas ha'Of and Olas ha'Of) and they bought four birds together, or gave money together to a Kohen (to buy and offer four birds), the Kohen may offer any (two) birds for Chata'os and the others for Olos (one of each for each woman).

Suggestion: This shows that R. Yosi holds that Yesh Breirah! (We say that retroactively, each bird offered for each woman belonged to her.)

Rejection (Rabah): No, the case is, they stipulated (Ri - when they bought the birds, which belongs to each woman. The birds were never mixed up.)

Objection: If so, this is obvious!

Answer: It teaches (Ri's text - that we do not decree on account of when they did not stipulate, for then Breirah would be required, and also) Rav Chisda's law:

Rishonim

Rambam (Hilchos Pesulei ha'Mukdashim 5:11): If anyone obligated to bring a Ken separated coins for it, he may use all the money for the Chatas or all for the Olah if he wants. Even if he said 'these coins are for my Chatas, and these are for the Olah', he can mix the money and buy both or just one from it. A Ken becomes Mefurash only when the owner buys it or when the Kohen offers it.

Rashi (Eruvin 37a DH keshe'Hisnu): The women stipulated that each bird will belong to the woman for whom the Kohen offers it.

Rebuttal (Ri, in Tosfos DH keshe'Hisnu): This relies on Breirah. We answered that they stipulated to show that R. Yosi can hold that Ein Breirah! Rather, when they bought the birds, they stipulated which belongs to each woman. The birds were never mixed up.

Defense (Tif'eres Yisrael, Kinim 3:4 Boaz 3): Rashi means that they stipulate that when each bird is offered, it will belong to the one for whom it is offered. Had they stipulated that it was hers retroactively, Breirah would be required.

Rambam (8:8): If two bought their Kinim together or gave the money for their Kinim together to the Kohen, he offers whichever he wants for the Chatas and whichever he wants for the Olah. This is because a Ken becomes Mefurash only when the owner buys it or when the Kohen offers it.

Question (Ri Korkus and Kesef Mishneh): Rav Chisda discusses only one woman. When there are two, perhaps both birds of Leah are offered for Olos! The Gemara in Eruvin suggested that R. Yosi must hold that Yesh Breirah. To reject this, we said that the women stipulated. Since the Rambam rules that Ein Breirah, he should require that they stipulate!

Answer #1 (Kesef Mishneh): The Rambam explains that when we conclude that the Mishnah teaches Rav Chisda's law, even if they did not stipulate it is as if they stipulated, so Breirah is not required.

Answer #2 (Ri Korkus): The Rambam explains the stipulation like Rashi (each bird will belong to the woman for whom it is offered). Breirah is not needed, for the birds were never distinguished before they were mixed. Surely it is as if they stipulated (so they will be able to offer the birds)! Since they bought together, it is as if each woman pardoned all or half of her money to the other, so that the other will do the same. Some say that since they stipulated from the start, the Kohen was their Shali'ach to divide the birds.

Me'iri (Eruvin 37a DH Shtei): The Gemara says that the women stipulated. This is not the Halachah. Rather, Stam, the women make the Kohen their Shali'ach to divide the birds, and they accept his division. Some texts do not say '(the case is that) they stipulated', rather, 'for (Stam,) they stipulated.'