Gemara

Beraisa: "V'Osahu Chatas" - the Goral (lottery) fixes the goat to be a Chatas, but Shem (calling it a Chatas) does not.

A Kal va'Chomer should have taught that Shem works. Shem fixes a bird to be a Chatas, but a Goral does not; a Goral fixes a goat to be a Chatas, all the more so Shem should work!

The verse teaches that only Goral works.

Rav Chisda: A Kan becomes Mefurash (specified, i.e. which bird is the Chatas and which is the Olah) only at the time the owner bought it, or (if he did not specify then) when the Kohen offers it.

Rav Simi Bar Ashi: He learns from "V'Lokchah Shtei Sorim..." and "V'Osah ha'Kohen..." (both verses say that one is for Chatas, one for Olah). The owner decides this at the time of purchase, or the Kohen decides at the time of Hakravah.

Question (Beraisa): "V'Osahu Chatas" - the Goral determines the Chatas, but Shem does not.

We should have learned from a Kal va'Chomer. Shem fixes a bird, but a Goral does not. A Goral fixes a goat, all the more so Shem should work!

The verse teaches that only Goral works.

Summation of question: Shem works (at a time when Goral does not, i.e. it is) not at the time of purchase nor at the time of Hakravah!

Answer (Rava): It means that regarding birds, Goral does not work even at the time of purchase or Hakravah, but Shem works at these times. Regarding the goats, Goral works not at the time of purchase or Hakravah, all the more so Shem should work at the time of purchase or Hakravah!

The verse teaches that this is not so.

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

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

Objection (Rav Sheshes): The Beraisa is mistaken, for it says that he was Mefaresh after he became rich. R. Elazar taught in the name of R. Oshaya that if an Ashir brought a Korban Oni for Tum'as Mikdash, he was not Yotzei (so surely, such Hafrashah is invalid)!

Correction (Rav Sheshes): We must fix the Beraisa to 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 taught in the name of R. Oshaya that if an Ashir brought Korban Oni for Tum'as Mikdash, he was Yotzei (so there is no reason to alter the Beraisa). How can he answer?

Answer #2: Instead of '(He was Makdish, became rich,) and later said...' it should say, '(He became rich,) and later was Makdish and said....' (We can add a word to a Beraisa without a compelling reason, for it often happens that a word gets forgotten - Rashi.)

Eruvin 37a - Mishnah - R. Yosi: If each of two women are obligated to offer a Kan 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: We say that each bird offered for each woman belonged to her retroactively. This shows that R. Yosi holds Yesh Breirah!

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

Objection: If so, this is obvious!

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

Rav Chisda: A Kan become Mefurash only at the time the owner bought it, or when the Kohen offers it.

Rishonim

Rambam (Hilchos Pesulei ha'Mukdashim 5:11): If anyone obligated to bring a Kan separated money for it, he may use all of the money for the Chatas or all for the Olah. Even if he specified 'this money is for the Chatas and this is for the Olah', he can mix them together and buy both together, or just one of them. This is because a Kan becomes Mefurash only at the time or purchase or at the time of Hakravas Kohen.

Question: The Rambam connotes that even designation of money at the beginning (for Chatas or Olah) does not take effect! It is difficult to say that he discusses one who was Makdish money, and only later specified that part is for Chatas. If so, why does he omit the law of money designated from the beginning?

Answer (Aruch l'Ner Kerisus 28a DH Ein Kinim): Rav Chisda only discusses designation of birds from the beginning. This suggests that designation of money at the beginning does not take effect. Rav Sheshes answered that the Beraisa means that he was Mefaresh money at the time of Hekdesh and it takes effect. This was only according to the questioner, i.e. even if you think that the Beraisa is reliable, it does not refute Rav Chisda. However, really the Beraisa is mistaken, and Perush of money even at the time of Hekdesh does not take effect.

Keren Orah (Nazir 26b DH u'Mikal): The final words of the Rambam (a Kan becomes Mefurash only at the time or purchase or Hakravah) suggest that even money can become Mefurash from the beginning.

Rashi (41a DH Ela Mai): Separation of money is (Mefaresh) like the time of buying birds.

Question (Sefas Emes DH she'Kevar): It is not clear why this is considered "V'Lokach" or "V'Hevi".

Rambam (ibid. 8:8): If two people bought their Kinim together or gave money for their Kinim to the Kohen, the Kohen can offer whichever ones he wants for Chatas and the others Olah. This is because a Kan becomes Mefurash only at the time or purchase or at the time of Hakravas Kohen.

Question: It was suggested (Eruvin 37a) that this is according to the opinion that Yesh Breirah. This was rejected by saying that the case was that they stipulated. Since the Rambam rules that mid'Oraisa Ein Breirah, he should require that they stipulated!

Answer (Kesef Mishneh): The Rambam holds that according to Rav Chisda, it is as if they stipulated (that whichever birds the Kohen will offer for Leah will be hers). Since they did not specify at the time of purchase, only Hakravah can determine which birds are for which woman.

Ri Korkus: Tosfos (Kinim 22b DH l'Eizeh) says that when one puts money into Shofaros (boxes from which Kohanim buy and offer Korbanos), it is as if he stipulated that Beis Din (of Kohanim) may do with the money as it sees fit.

Question (Yam Shel Shlomo Bava Kama 5:32 (p.47)): R. Yehudah says that there was not a Shofar for Kinei Chovah. We are concerned lest we learn that someone who gave money died, which mandates that his Chatas die, and since we cannot determine which is his Chatas because Ein Breirah, all must die. Elsewhere, R. Yehudah holds that Yesh Breirah!

Answer (Yam Shel Shlomo, ibid.): Yesh Breirah applies only when the Isur was never specified, e.g. 'the Terumah I will separate from this pile' or 10 sheep traded for nine sheep and a dog (they never specified which sheep corresponds to the dog). But if an Isur became mixed with Heter, we cannot use Breirah to remove one and say that it was the Isur, for perhaps we did not remove the Isur! If Chata'os became mixed, and the owner of one died, all would have to go to Yam ha'Melach. But since a Kan (or money) becomes Mefurash only at the time or purchase or Hakravah, a person's money could be used all for Olos, therefore the stringency of Chatas she'Mes Ba'alav does not apply.

Me'iri (Eruvin 37a DH Shtei): Even though the Gemara says that they stipulated, this is not the Halachah. Rather, in any case it is as if they stipulated, because a Kan becomes Mefurash only at the time or purchase or of Hakravah.