Gemara

55b: The following shows that R. Yehudah holds that Ein Breirah:

(Mishnah - R. Meir): One who buys wine from Kusim (and is not able to separate the tithes before drinking) says 'The two Lugim that I will later separate should be Terumah. Ten Lugim (that I will separate) should be Ma'aser Rishon, and nine Lugim should be Ma'aser Sheni.'

He is Meichal (redeems the Ma'aser Sheni; alternatively, mixes the wine) and may drink immediately;

R. Yehudah, R. Yosi and R. Shimon say, he must separate the tithes before drinking.

Rejection: Really, R. Yehudah holds that Yesh Breirah. He argues with R. Meir for a different reason:

Beraisa - R. Yehudah, R. Yosi and R. Shimon (to R. Meir): He may not drink before separating the tithes, lest the barrel break before he separates them, and retroactively he drank Tevel!

R. Meir: We are not concerned until it breaks.

Rather, the following shows that R. Yehudah holds that Ein Breirah:

Ayo - Beraisa - R. Yehudah: A person cannot stipulate about two things simultaneously (e.g. to place two Eruvin and decide on Shabbos which is valid);

He can say 'If a Chacham comes from the east, my Eruv is in the east; if from the west, it is in the west'; but he cannot make both stipulations.

Question: Surely, (R. Yehudah holds that) he cannot stipulate about both (and decide on Shabbos) because Ein Breirah. For the same reason, he should not be able to stipulate about when a Chacham comes from one direction!

Answer (R. Yochanan): The case is, the Chacham already came (before Bein ha'Shemashos, but the Me'arev did not know in which direction. It is already determined, so it does not depend on Breirah).

Eruvin 37b - Suggestion: Perhaps R. Shimon holds that Yesh Breirah for mid'Rabanan laws (such as Eruv), but Ein Breirah for mid'Oraisa laws (Ma'aser of wine!

Rejection: Rav Yosef holds that the Tana'im do not distinguish between mid'Oraisa and mid'Rabanan regarding Breirah.

Gitin 47a - Beraisa - Rebbi: If a Yisrael and a Nochri bought a field together, the produce is a mixture of Chulin (produce that need not be tithed) and Tevel;

R. Shimon ben Gamliel says, the Nochri's produce is Chulin and the Yisrael's is Tevel.

They argue about Breirah (R. Shimon ben Gamliel says that each partner receives his own share. Rebbi says, each owns half of all the produce. When they divide up, it is as if they sell to each other.)

Beitzah 38a: R. Oshaya holds Ein Breirah regarding mid'Oraisa laws. Regarding mid'Rabanan laws he holds that Yesh Breirah.

The Halachah follows R. Oshaya.

Rishonim

Rif (Beitzah 21a) and Rosh (Beitzah 5:7): The Halachah follows R. Oshaya, who holds that Ein Breirah regarding mid'Oraisa laws, but Yesh Breirah for mid'Rabanan laws.

Rambam (Hilchos Ma'aser 7:1): If one has 100 Lugim of wine that is Tevel mid'Oraisa and said 'The two Lugim that I will later separate should be Terumah, 10 Lugim Ma'aser Rishon and nine Lugim Ma'aser Sheni', he must separate them before drinking. Since it is Tevel mid'Oraisa, if he drinks now and separates later it is not considered as if they were separated when he drank.

Radvaz: The Mishnah discussed one who bought wine from Kusim. Their wine was considered Vadai Tevel. If one bought from an Am ha'Aretz, it is Demai (Safek). The Chiyuv to tithe it is mid'Rabanan, so one may rely on Breirah.

R. Akiva Eiger (Gilyon ha'Rambam to Terumos 1:20, brought in Frankel): The Gemara (Eruvin 37b) calls Ma'aser of wine of Kusim mid'Oraisa according to R. Shimon, even though he holds that Kusim are Nochrim (Garei Arayos), and Miru'ach of a Nochri is Chayav only mid'Rabanan! This is because the original Chiyuv was mid'Oraisa (Tosfos Yeshanim Bechoros 11b DH Tevalim). The Rambam totally exempts Miru'ach Nochri of his own produce. He must say that in the Mishnah the Kusi bought grapes from a Yisrael after they grew a third, or he bought and resold wine of a Yisrael.

Ri Korkus: Some say that the Gemara rules like R. Oshaya regarding mid'Rabanan laws, but the Halachah is Yesh Breirah even for mid'Oraisa laws. We learn from Nedarim (45b, regarding a Chatzer of partners) and the Mishnah of two Lugim (those who forbid do so because we are concerned lest the barrel break). The Rambam holds that they address R. Meir according to his reasoning. We forbid because Ein Breirah. Even you should admit, lest the barrel break!

Rambam (ibid. 9:7): If Reuven was invited to eat on Shabbos by someone whom he does not trust regarding Ma'aser, before Shabbos Reuven says 'What I will separate tomorrow should be Ma'aser (Rishon); the rest of the Ma'aser (Rishon) is next to it. This that I made Ma'aser (first) is Terumas Ma'aser on the other Ma'aser. Ma'aser Sheni is in the north (or south), and it is redeemed onto the coins.'

Such a stipulation is permitted regarding Demai, even though it is not in his Reshus. One may not stipulate about Vadai Tevel unless it is in his Reshus.

Rambam (Hilchos Terumos 1:20): If a Yisrael and a Nochri owned a field together, every stalk is a mixture of Tevel and Chulin. This is even if they divided the field before harvesting and the Nochri did Miru'ach on his share and it is Chayav mid'Rabanan.

Radvaz: We say Ein Breirah because the primary Chiyuv is mid'Oraisa.

Gra (YD 331:26): Because the produce was already Chayav mid'Oraisa, we say Ein Breirah.

Rambam (21): This is in Eretz Yisrael, where Ma'aseros are mid'Oraisa, so Ein Breirah. If they were partners in a field in Surya, the Nochri's share is Chulin. This is even if they divided the harvested produce, because Terumah is mid'Rabanan in Surya, so Yesh Breirah.

It seems that nowadays this applies even in Eretz Yisrael because the Chiyuv for Terumah and Ma'aser is only mid'Rabanan.

Rambam (Hilchos Girushin 3:4): Even if a man (with two wives named Leah) told a scribe 'write a Get, and I will decide to which wife I will give it', and he gave it to one of them, it is Safek Girushin.

'Magid Mishnah': The Rambam holds that Yesh Breirah. He calls it Safek Girushin because the Mishnah says that the Get is Pasul.

Kesef Mishneh: The Gemara says that mid'Rabanan Yesh Breirah. This connotes that we are in doubt whether or not Yesh Breirah, and we are lenient regarding mid'Rabanan laws. Regarding mid'Oraisa laws we are stringent to say that (perhaps) there is not Breirah.

Rebuttal (Yam Shel Shlomo Bava Kama Perek 5 Dinei Breirah (p.47b)): The Rambam (Hilchos Shemitah 11:20) rules that brothers who divided an inheritance return their portions and divide the property again in Yovel. If it is a Safek whether or not Yesh Breirah, we would not take property from them. Perhaps each brother inherited the proper portion, and they need not redivide in Yovel!

Poskim

Shulchan Aruch (YD 331:11): In Eretz Yisrael, Terumah is mid'Oraisa, so Ein Breirah. Therefore, if a Yisrael and a Nochri owned a field together, every stalk is a mixture of Tevel and Chulin. This is even if they divided the field before harvesting and the Nochri did Miru'ach on his share and it is Chayav mid'Rabanan.

Shulchan Aruch (ibid.): If they were partners in a field in Surya, the Nochri's share is Chulin. This is even if they divided the harvested produce, because Terumah is mid'Rabanan in Surya, so Yesh Breirah. It seems that nowadays this applies even in Eretz Yisrael because the Chiyuv for Terumah and Ma'aser is only mid'Rabanan.

Rema (2): Some say that nowadays Terumos and Ma'aseros are mid'Oraisa in Eretz Yisrael, but the custom is not like this.