Gemara

(Mishnah - R. Yosi): If Reuven paid part of his debt to Shimon, and fixed a date and gave the document to Levi and said 'if I do not pay the rest by this date, give the document to Shimon (who may then collect the full amount)', and Reuven did not pay in time, Levi gives the document to Shimon;

R. Yehudah says, he does not give it.

R. Yosi says that Asmachta (an exaggerated promise) is binding. R. Yehudah holds that it is not.

(Rav Nachman): The Halachah is (some texts - not) like R. Yosi.

When people would come in front of R. Ami, he would say 'R. Yochanan taught that the Halachah follows R. Yosi. How can I argue?!'

The Halachah does not follow R. Yosi.

Nedarim 27a (Rav Huna): If one had documents in his favor in Beis Din, and said 'if I do not return within 30 days, these proofs should be void', and an Ones prevented him from returning in time, his proofs are void.

Question: Rav Nachman said that the Halachah does not follow R. Yosi, who says that Asmachta acquires!

Answer: Here is different. Since he said that the proofs should be void, this is like an admission that they are invalid.

The Halachah is, Asmachta acquires when there is no Ones, and they acquired from him in an esteemed Beis Din.

Rishonim

Rif and Rosh (10:19): The Halachah does not follow R. Yosi. Asmachta acquires when there is no Ones, and they acquired from him in an esteemed Beis Din. A Ga'on says that this is only when he deposited his proofs in Beis Din. Presumably, this is correct.

Nimukei Yosef (Nedarim 9b DH v'hilchesa): Rav Huna's case wzs not really Asmachta, for his Din was based on the proofs he agreed to! The esteemed Beis Din is an expert who can judge alone, force people to come to be judged, make money Hefker, and fine people who seek to evade the Din. The same applies to three regular judges. Kinyan in Beis Din does not help for real Asmachta, which does not depends on Beis Din! Rav Hai Gaon says so; this is the Ga'on cited in the Rif.

Rosh (ibid): Tosfos rules that even without depositing his proofs, Asmachta acquires in an esteemed Beis Din. Our custom is like this. Rabbeinu Meir says that the esteemed Beis Din must be proficient in laws of Asmachta.

Rambam (Hilchos Mechirah 11:5): If Reuven paid part of his debt and gave the document to Ploni, and said 'if I will not pay (the rest) by day Almoni, give the document to the lender', and the time came and he did not give, Ploni should not give the document to the lender, for this is Asmachta.

Rambam (13): If they acquired from him in an esteemed Beis Din it acquires, if he deposited his proofs in Beis Din and there was no Ones.

Ran (Nedarim 27b DH v'Hu): The Rambam (Perush ha'Mishnayos 168a) says that the Beis Din must have Semichah in Eretz Yisrael. If so, the Gemara should have said 'a Beis Din Mumcheh' (expert)!

Hagahos Maimoniyos (8): In Nedarim we say that if they acquired from Reuven about Asmachta in an esteemed Beis Din, it is binding, if it was not Ones. Also Rav Tzemach Gaon, the Rashbam and Rivam, R. Tam, Ri, my Rebbi and Avi ha'Ezri say so. Rav Hai Gaon says that whenever it says that Asmachta acquires, this is R. Yosi's opinion, and the Halachah does not follow him. How can he oppose the Gemara's ruling in Nedarim?! The Rif and R. Chananel rule like unlike Rav Hai Gaon.

Rosh (Nedarim 3:10): Some say that Asmachta acquires only in a case like Rav Huna's, in which he deposited his proofs in Beis Din. If it always acquired (when there is no Ones, and they acquired in an esteemed Beis Din), why was the Halachah taught in Nedarim? It should have been taught in Bava Basra, where R. Yosi and R. Yehudah argue! This is not a proof. It was taught here, for here we discussed Ones. It applies to all Asmachta.

Ran (Nedarim 27b DH v'Hilchesa): Asmachta does not acquire even due to a small Ones, e.g his son became sick. We need not teach about a big Ones. The Gemara compared this to vows. Just like one who vows did not intend if (he will not fulfill the Tanai because) his son is sick, one did not intend to neglect his son to go to Beis Din.

Poskim

Shulchan Aruch (CM 55:1): If Reuven paid part of his debt and gave the document to Ploni, and said 'if I will not pay by day Almoni, give the document to the lender, and he did not pay by then, Ploni should not give the document to him, for this is Asmachta (i.e. he obligated himself based on his will, it is partially in his hands, and he relied (that he will fulfill it, so) that the obligation will not take effect, and he did not resolve to be Makneh), and it does not acquire. If they acquired from him (Chalipin) in an esteemed Beis Din, it is binding, if he left his proofs in Beis Din. This is if there was no Ones. If he left his document or receipt in Beis Din, and they acquired from him that if he does not come by day Almoni, it should be given to his opponent, and he did not come before that day, we give it.

Beis Yosef (Sof Siman 54, DH u'Mah she'Chosav Rabeinu b'Shem ha'Ramah): The Ramah says that depositing proofs helps only if he said 'my proofs will be Batel (if I do not fulfill my promise)', and an esteemed Beis Din acquired from him. I.e. it must be exactly like Rav Huna's case. The Tur connotes that the Rif holds that it is enough to deposit the proofs, even not in Beis Din, even if he did not say 'my proofs will be Batel.' I say that the Rif agrees with the Ramah, since he holds that Asmachta acquires only in cases like that of Rav Huna.

Gra (1): Since it says in Nedarim 'and the Halachah is', this shows that it refers to the case given (of Rav Huna).

Shulchan Aruch (ibid): If he was detained due to the river or sickness, they do not give it. The same applies to all similar cases.

Shach (1): I proved in YD 232:20 that this refers to an Ones that is common but not so common, and all the more so if it is not common at all, it is Ones for vows and monetary matters. A common Ones is not Ones. He should have stipulated! The Rosh and R. Yerucham say that if the river got bigger due to rain or melting snow, which is uncommon, this is Ones. If there was no ferry to cross it, this is common, and he should have stipulated. Maharshach (2:45) argues with the Rosh and R. Yerucham. He errs.

Mishneh l'Melech (Hilchos Shevuos 3:1): Maharshach holds that Ones always exempts, even if it is uncommon except for Get. He asked why R. Yerucham said that the Mishnah in Nedarim discusses a river that enlarged due to rain and melting snow, which is uncommon. Even a common Ones is Ones! Maharshach proved that a common Ones is not Ones from Teshuvas ha'Rosh about a Shiduch, and Rashi, who discusses an evident Ones, like the ferry ceasing. This is no proof. The Rosh says that there is an Umdena (we know his intent). Also in Rashi's case, surely one forfeits his proofs only if he will not come without any Ones. Maharival holds that a common Ones exempts only when there is an Umdena (that he did not intend in such a case). This is unlike R. Yerucham and the Rosh, who say that the Mishnah in Nedarim discusses an uncommon Ones, even though there is an Umdena that he did not intend to forbid his friend if Ones prevents him from eating with him. Also, why did the Gemara challenge Rava from the case of 'if I will not come within 30 days'? There is different, for there is no Umdena. When one left his proofs in Beis Din, there is an Umdena! The Rashba (771) says that a common Ones is not Ones. Mahara Sason explains that he should have stipulated, but a semi-common Ones is Ones. R. Yerucham and the Rosh said that the Mishnah discusses a semi-common Ones, for there is not a good Umdena. Rav Huna holds that even a totally uncommon Ones does not exempt. This applies to only to one who forfeits his proof, for he admits that his proof is invalid. An admission is like 100 witnesses. Rava argues. He holds that it is not admission, rather, pardon. The Umdena is that he pardons only if he will not fulfill, without any Ones. Or, Rava could agree that it is due to admission, but only if there was no Ones. Pnei Moshe proves that Rava discusses even a common Ones from the case of a Get 'on condition that I not return within 12 months'. This is astounding. The beginning of Kesuvos says that death is not called common!

Shulchan Aruch (ibid): This is if it is in an esteemed Beis Din.

Beis Yosef (DH Mi): A case occurred in which Shimon had two documents against Reuven, for 500 each. Reuven paid one, left both documents with Ploni, and said 'if I will not pay the other by this day, return both to Shimon.' He did not pay in time. Rabbeinu Meir said that an esteemed Beis Din is three who know what is Asmachta (Rosh 72:4). E.g. it depends on whether he exaggerated, and whether he was able to do what he accepted. Since they know laws of Asmachta, and he acquired unlike Asmachta, Hefker Beis Din is Hefker, and it is binding. Here, there was no Kinyan, and in any case it was not in an esteemed Beis Din, so Reuven owes only 500.

Beis Yosef (ibid., DH veha'Rashba): The Rashba (3:60) says that an esteemed Beis Din must have power to make money Hefker. The Magid Mishneh (Hilchos Mechirah 11:13) says that the Rashba does not require Semichah, as long as they are esteemed to make Hefker, e.g. experts who judge the Rabim. The Nimukei Yosef (78a DH Gemara) says that it is one who can judge monetary cases alone, like it says in Nedarim.

Rema: Some say that he need not deposit his document, since they acquired in an esteemed Beis Din.

Gra (3): This opinion holds that it says 'and the Halachah is' due to the case of Ones.