(Mishnah): Before the Mishkan was erected, Bamos were permitted, and Avodah was done by the firstborns;

After the Mishkan was erected, Bamos were forbidden, and Kohanim did the Avodah.

Kidushin 8a: Rav Kahana took a turban in place of the five Sela'im for Pidyon ha'Ben (redemption of a firstborn son).

Chulin 131b: Ula would give Matanos (the foreleg, jaw and stomach of a Chulin Behemah) to a Kohenes.

Question (Rava - Mishnah): The Minchah of a Kohenes is eaten (except for a Kometz (handful), which is burned on the Mizbe'ach). The Minchah of a Kohen is Kalil (entirely burned on the Mizbe'ach).

If "Kohen" included Kohenes, "Kol Minchas Kohen Kalil Tiheyeh Lo Se'achel" would apply also to Minchas Kohenes!

Answer (Ula): Just the contrary! The Torah had to write "Aharon u'Vanav" to teach that this applies only to male Kohanim. Otherwise, a Kohenes would be included!

(Beraisa - Tana d'Vei R. Yishmael): "Aharon u'Vanav" teaches that Minchas Kohen is Kalil, but Minchas Kohenes is not. We learn to Matanos (about which it says only "Kohanim," that a Kohenes is excluded).

(Beraisa - d'Vei R. Eliezer ben Yakov): The Matanos may be given to a Kohen or Kohenes;

"Kohen" excludes females. It says "Kohen" twice in the Parshah. Two exclusions (for the same matter) come to include.

Rav Kahana (was a Yisrael married to a Kohenes. He) received and ate Matanos due to his wife, and so did Rav Papa, Rav Yemar, and Rav Idi bar Avin.

(Ravina): The Halachah follows Ula.

Rambam (Hilchos Bikurim 1:10): Pidyon ha'Ben is give to a male Kohen, because it says "Aharon u'Vanav."

Rosh (Hilchos Pidyon Bechor, Sof Bechoros, Siman 4): One may not give a Bechor Behemah or Pidyon ha'Ben to a Kohenes. Ula would give Matnos Kehunah to a Kohenes. Rava challenged this, and Ula answered that "Aharon u'Vanav" excludes females. In Bamidbar (3:51), it says "Moshe gave the redemption of the firstborns (above the number of Leviyim) to Aharon u'Vanav." A Hekesh equates human Bechoros with those of donkeys. This is unlike Rashi, who says in Kidushin that Rav Kahana was not a Kohen, rather, he received Pidyon ha'Ben due to his wife, who was a Kohenes.

Ma'adanei Yom Tov (50): Also the Beis Yosef cites the Rosh to say 'this is unlike Rashi.' However, it seems that it say 'Ri' (like the Rosh said in Teshuvah 49:3 - PF).

Note: Also the Rashba (1:836 citing the Ramban) brought this proof.

Tosfos (Kidushin 8a DH Rav): Our Gemara connotes that Rav Kahana was a Kohen. However, Pesachim 49a connotes that he was not, for he said that he was exiled because he married a Kohenes (and he was not worthy to do so). We can say that there were two Chachamim named Rav Kahana (and the one who received Pidyon ha'Ben was a Kohen). Alternatively, he received due to his wife (a Kohenes), just like Rav Chisda ate (Matanos) due to his wife.

Question (Pnei Yehoshua Kidushin 8a DH Tosfos): Tosfos holds that just like there is an opinion that one gives Matanos to a Kohen, and even to a Kohenes, the same applies to Pidyon ha'Ben. I did not find anyone else who says so. One may give to a Kohenes only where the Torah taught so. We see so only regarding the foreleg, jaw and stomach. This requires investigation.

Answer (R. Akiva Eiger Kidushin 8a DH Shulchan): The law of whether one may give Pidyon ha'Ben to a Kohenes is not explicit. Ula excludes a Kohenes from the law of Kalil due to Aharon u'Vanav. If so, Pidyon ha'Ben is like Matanos, and one may give to a Kohenes. R. Eliezer ben Yakov learns from two exclusions that one may give Matanos to a Kohenes, but he has no source to give Pidyon ha'Ben to a Kohenes. We rule like Ula; seemingly, this includes other Matanos, unless we say that we rule like Ula, but not for his reason. Perhaps this is why Rashi in Chulin (132a DH Rav) explained that "Kohen" includes a Kohenes (and not due to two exclusions), in order to explain why Rav Kahana received Pidyon ha'Ben. What was the Pnei Yehoshua's question? Perhaps Rav Kahana holds like Ula!

Teshuvas Chasam Sofer (YD 301): Why didn't Tosfos accept the Rosh's proof? In Parshas Korach, it does not say Aharon u'Vanav. We do not learn about the Mitzvah for all generations from the redemption in the Midbar. Even though we learn from the Midbar to exempt sons of Kohanim and Leviyim (Bechoros 4a), we are forced to say that one can distinguish these.

Aruch ha'Shulchan (YD 305:3): Aharon u'Vanav is written regarding Pidyon ha'Ben also for all generations! Bamidbar 18:8 says "Nosati Lecha.. ul'Vanecha", and the Parshah proceeds to discuss Pidyon ha'Ben (18:15,16)!

Tosfos (Sotah 23b DH Kohen): The Minchah of a Kohenes married to a Yisrael is not Kalil, for "Kohen" excludes a Kohenes. The Yerushalmi asked why we do not similarly expound that slaves of a "Kohen" eat Terumah, but not slaves of a Kohenes. It answered that "ha'Kohen ha'Mashi'ach Tachtav mi'Banav" (Vayikra 6:15, just before it says that a Kohen's Minchah is Kalil) excludes a Kohenes, for her son does not fill her place. In Chulin, when we suggested that "Kohen" should exclude a Kohenes from Matanos, we could have given this answer. Alternatively, a Kohenes receives Matanos because there are two verses to exclude her.

Ramban (Vayikra 6:7-11): Moreh Nevuchim (3:46) explains that a Kohen's Minchah is Kalil because he offers it himself. If he would offer his Minchah and eat it, it would be as if he did not offer anything, since only the frankincense and Kometz (a very small part) go on the Mizbe'ach. Therefore, it is totally burned.

Chasam Sofer: This is the reason why a Kohenes' Minchah is not Kalil, because she cannot offer it herself. The Rambam (Hilchos Ma'aseh ha'Korbanos 12:10) said that her Minchah is not Kalil. The Ra'avad asked that the Rambam already taught this. The Kesef Mishneh answered that the Rambam teaches that this is even if she is Penuyah (single), and not married to a Yisrael. If the Gemara did not need to teach that a Penuyah is no different, why did the Rambam need to teach this? If the Gemara distinguishes, what is the Rambam's source to equate them? Rather, the Gemara holds like the opinion that expounds the reason for Mitzvos. If so, surely the same applies to any Kohenes. The Rambam holds like the opinion that does not expound the reason for Mitzvos. One might have thought to distinguish; the Rambam teaches that we do not, due to Aharon u'Vanav or the Yerushalmi's Drashah. If we expound the reason for Mitzvos, surely a Kohenes does not receive Pidyon ha'Ben. Hash-m gave the money to Kohanim who can serve, for the Leviyim were chosen to replace the Bechoros, like it says in Zevachim.

Shulchan Aruch (YD 305:3): One gives Pidyon ha'Ben to a Kohen.

Tur: One redeems his son from a Kohen, but not from a Kohenes.

Beis Yosef (DH u'Mah she'Chosav she'Yifdenu): This is like the Rosh. He brought a proof from Chulin, unlike Rashi.

Chasam Sofer (ibid.): Someone said in my name that one may give Pidyon ha'Ben to a Yisrael married to a Kohenes. This is wrong. I was at a Pidyon ha'Ben, and someone blessed without asking permission from the Kohen. Someone asked 'how can there be Pidyon ha'Ben without a Kohen?!' I said that according to Tosfos, one may give to a Yisrael married to a Kohenes, and that I give the foreleg, jaw and stomach to my brother-in-law, who is a Yisrael married to a Kohenes. I would not decide between Tosfos and the Rosh regarding Pidyon ha'Ben. Even if I would, one may not act upon it, since I was not asked in practice. I merely said so in passing; Divrei Chachamim make one wise.

Chasam Sofer: In Pesachim, Tosfos gave only the answer that Rav Kahana received due to his wife. In Chulin (132a), Tosfos gave only the answer that the Rav Kahana who received Pidyon ha'Ben was a Kohen. The Tur rules like the Rosh, and Sefer ha'Chinuch brought the Rosh's proof. We do not abandon them due to the Safek of Tosfos. However, Tosfos in Sotah cites the Yerushalmi, which says that regarding a Minchah, we do not exclude a Kohenes from "Kohen", rather, from "Tachtav mi'Banav." This is unlike the Bavli, which learns from Stam "Aharon u'Vanav." The Yerushalmi holds that u'Vanav includes daughters. Regarding Tum'ah, we exclude daughters from "Bnei Aharon", i.e. because it is extra, but not from the simple meaning, like the Mizrachi says (Vayikra 21:1 DH Bnei). This is why another Drashah was needed for Minchah. We can say that Rav Kahana received Pidyon ha'Ben for his wife because he holds like the Yerushalmi, unlike the Bavli. Perhaps the Halachah follows him, for he acted upon this.

Chasam Sofer: How can one give Matanos Kehunah, and all the more so Pidyon ha'Ben, to a Kohenes married to a Yisrael? He husband has rights to the Peros, so Shevet Kehunah did not receive the full amount, unless one gives on condition that her husband has no rights to it. Perhaps the Amora'im who ate Matanos due to their wives ate only Matanos from their own animals, but not from others', due to this question. The Ran, in Perek 10 of Chulin (I was not able to find this - PF) was unsure about this. The Tur (YD 61) said that one may give Matanos to a Kohenes married to a Yisrael; and even her husband is exempt. The Taz (10) asked why the Tur did not say that her husband exempts one who gives to him! Perhaps it is due to my reasoning.

Pischei Teshuvah (5, citing Chasam Sofer ibid.): If one cannot find a Kohen on the day for Pidyon ha'Ben, and he does not want to delay the Mitzvah, he can give to a Kohenes, without a Berachah, with intent that he is not Yotzei through this if he will find a Kohen. If he finds a Kohen, he redeems with a Berachah. We make such stipulations with R. Tam Tefilin and saying the evening Shma before dark. If it is hard to give the money twice, he can give to the Kohenes on condition that she return it to him.