Gemara

(Abaye): A Yisrael may not smell a Nochri's wine through Bas Tiha. a hole in the cork, or a straw partially inserted in a barrel).

(Rava): He may smell it.

Abaye holds Re'ach Milsa Hi (smell is important). Rava disagrees.

Pesachim 76b (Rav): If fat Shechutah (slaughtered meat) was roasted with lean Neveilah meat, it is forbidden.

The Neveilah absorbs fat, and then it gives off a smell.

(Levi): We permit even lean Shechutah roasted with fat Neveilah.

This is because it absorbs a mere smell. Re'ach Lav Milsa Hi.

(Rav Kahana brei d'Rav Chinena - Beraisa): If bread was baked in an oven with Tzeli (roasting meat), it may not be eaten with Kutach (a dairy dip).

A case occurred in which fish was roasted with meat. Rava of Parzakiya forbade eating it with Kutach. Mar bar Rav Ashi forbade eating it even with salt (i.e. alone), for a mixture of fish and meat can cause odor and Tzara'as.

Chulin 111b (Chizkiyah): The Halachah is that fish that were put (when hot) in a bowl (used for meat) may be eaten with milk.

Yevamos 81b (Beraisa): If a Tahor piece of a Chatas or Lechem ha'Panim was mixed with 100 Tahor Chulin pieces, all agree that it is not Batel.

82a (Rav Ashi): This refers to Davar she'Yesh Lo Matirim (it is permitted in another situation). It is never Batel, even in 1000 parts of Heter.

Rejection: This is wrong! For a Kohen, the piece is always permitted. For a Yisrael, it is always forbidden!

Rishonim

Rif (Chulin 32a): Rabanan rule like Levi. Rav holds like he taught, that a piece that absorbed Isur becomes (totally forbidden,) like a Neveilah, and forbids all other pieces. The Gemara said that this is like R. Yehudah, who says that Min b'Mino is not Batel. We rule that all Isurim are Batel in 60, even Min b'Mino, and all the more so a mere smell. The Beraisa of bread baked with meat, and the ruling about fish roasted with meat are even like Levi. Since one can eat them without Kutach, to permit them with Kutach is like permitting to bake them together. Levi permits only b'Di'eved! Also, bread baked with meat can be eaten alone, so it is like Davar she'Yesh Lo Matirim. It is not Batel even in 1000 parts of Heter. One part in 1000 is like a mere smell; it is not Batel because Yesh Lo Matirim, but not because the Halachah follows Rav.

Question (Ran DH v'Chosavtiv): We permit meat and milk whenever it did not give taste. If fish came in a pot in which meat was cooked, one may eat the fish with Kutach, because it absorbed only Nat Bar Nat (a taste of meat from the pot, which absorbed a taste from the meat). Even though one could eat it without Kutach, we do not forbid due to Davar she'Yesh Lo Matirim, for it is always forbidden with Kutach. Davar she'Yesh Lo Matirim is only when it will be totally permitted later, like an egg laid on Yom Tov. Why was the Rif bothered by the Beraisa of bread baked with meat, and the ruling about fish roasted with meat? Even if these were unlike Levi, Levi is a Tana who taught Beraisos (he can argue with Beraisos)! Also the ruling is not difficult. Rava is cited constantly in the Gemara. His teaching overrides the ruling of Rava of Parzakiya. (Mar bar) Rav Ashi forbade eating it even by itself due to danger. Also, Levi could agree to these. The smell of meat is felt in them. One who eats them might think that actual meat was absorbed. If he eats it with Kutach, it seems like meat and milk. Therefore, it is forbidden. Kosher meat roasted with Neveilah is different, for one does not smell or taste the Neveilah in the Kosher meat. Also, perhaps we are more stringent about meat and milk than other Isurim, for people do not distance from it, since each of them is permitted by itself. We forbid putting them on a table together, unlike other Isurim. One may eat at a table with a Nochri who puts Yayin Nesech or other Isurim on the table. Therefore, we decreed about bread baked with meat. It was not due to Re'ach Milsa Hi. If it were, we would forbid eating it by itself, like we totally forbid bread baked in an oven smeared with lard (Pesachim 30b), for one normally bakes for many days. If we permit him to eat it by itself, he will come to eat it with Kutach. Rather, since letter of the law the bread is permitted even with milk, we do not forbid it by itself, for this would be a Gezerah to guard a Gezerah. All forbid to eat it with milk, due to the severity of meat and milk.

Rambam (Hilchos Ma'achalos Asuros 9:23): If bread was baked or fish was roasted in one oven with roasting meat, one may not eat it with milk.

Rambam (15:33): One may not roast Kosher meat with Neveilah in one oven, even if they do not touch each other. If he roasted them, together, the Kosher meat is permitted, even if the Asur meat was very fatty and the Kosher meat was very lean. Smell does not forbid. Only the taste of Isur forbids.

Rosh (Avodah Zarah 5:8): The Rashbam in the name of Rashi and Bahag follow Levi, for he holds like Rava. R. Tam rules like Rav.

Poskim

Shulchan Aruch (YD 108:1): One may not roast Kosher meat with Neveilah in one oven, even if they do not touch each other. If he roasted them, together, it is permitted, even if the Asur meat was very fatty and the Kosher meat was very lean. If a big oven that holds 12 Esronim (an Isaron is the volume of 43 and a fifth eggs), and the opening is open, one may roast them together, as long as they do not touch. If one is covered in a pot or with dough or similar matters, one may roast them together even in a small oven whose opening is closed.

Rema: The same applies to meat with milk. The custom is to be stringent l'Chatchilah, even in a big oven, and lenient b'Di'eved, even in a small oven. If one baked bread with meat, one may not eat it with milk if he has other bread.

Shach (5): Toras Chatas (35:1) connotes that this is even if it is a big oven and it is slightly open.

Gra (6): This is like Isur v'Heter ha'Aruch (39:3). He holds that Tosfos distinguishes between big and small ovens only according to Rav, but we hold like Levi, so there is no difference. However, all the Poskim write like the Mechaber.

Rema (ibid.): Similarly, if a Nochri baked bread with Isur, one may not buy the bread if there is other bread, for this is considered l'Chatchilah.

Taz (4): Toras Chatas (35:1) says that the custom is to buy from Nochrim foods, to which Bishul Akum does not apply, cooked in their Kelim, because Stam Kelim are not Bnei Yoman (Keli, used for hot Isur in the last 24 hours). Even though l'Chatchilah we forbid Nosen Ta'am li'Fgam, buying is not considered l'Chatchilah. This is why in Krako our custom is to buy water nuts or other things that Nochrim cook.

Gra (8): Levi's Heter was for what a Yisrael cooked.

Rema (ibid.): If he does not have a liberal amount of other bread, both are permitted, for this is considered b'Di'eved.

Gra (9): This is unlike the Rif, who said that Rav Kahana's Beraisa forbids due to Davar she'Yesh Lo Matirim, which is never Batel, and Levi agrees. The Rif holds that Rav holds like he taught, that Min b'Mino is not Batel. Since we hold that it is Batel in 60, the Halachah does not follow Rav, but regarding Yesh Lo Matirim even Levi agrees to Rav. However, they challenged the Rif, for this is not Davar she'Yesh Lo Matirim, like it says in Yevamos 82a. Also, Davar she'Yesh Lo Matirim is Batel b'Eino Mino (102:1). Also, if so why do we permit (with milk) fish that came in a hot (meaty) pot? Also, Rava permits Bas Tiha by itself. There are answers to these questions, but the first opinion in the Rif is primary. The Rema (Darchei Moshe and Toras Chatas) observes that we permit buying oil and honey of Nochrim due to Nosen Ta'am li'Fgam. We do not call this l'Chatchilah! It is not clear why the Rema permits meat and milk. Since it can be eaten without milk, this is l'Chatchilah, like the Rif wrote! The Rambam forbids without distinction, even though he rules like Levi. Also the Gemara Stam forbids with Kutach.

Rema (ibid): Some say that we permit smell even b'Di'eved only if the oven is open a little on the side or at the top where the smoke exudes. One should not be stringent if it will cause a loss b'Di'eved, even if it is totally sealed.

Shach (8): The Rema is lenient to avoid a big loss (Toras Chatas 35:4). Even regarding food cooked in a pot that was not Ben Yomo, the Rema (Sa'if 2) is lenient only to avoid a big loss.