Gemara

(Mishnah - Beis Shamai): If one said 'this cow said 'I will be a Nazir if I will get up' or 'this door said 'I will be a Nazir if I will be opened'', he is a Nazir;

Beis Hillel say, he is not a Nazir.

R. Yehudah says, Beis Shamai discuss only one who said 'this cow is Alai a Korban if it will stand.''

(Rava): The case is, a cow was crouching in front of him: He said 'I am a Nazir from its flesh if it will not stand', and the cow stood on its own.

Beis Shamai explain, he himself intended to make the cow stand, and he did not do this (therefore he is a Nazir).

Beis Hillel say, he just wanted that the cow get up, and this was fulfilled.

Rishonim

Rambam (Hilchos Mechirah 22:15): The law of Hekdesh, Aniyim and Nedarim is unlike that of regular people. If one said 'all offspring of my animal will be Hekdesh to Bedek ha'Bayis' or 'forbidden to me' or 'for Tzedakah', even though it does not become Kodesh because it is Lo Ba l'Olam, he must keep his word, due to "k'Chol ha'Yotzei mi'Piv Ya'aseh."

Rivash (2:95, cited in Bedek ha'Bayis YD 258 DH uvi'Teshuvos): Fines that one obligates himself, even to give to Aniyim, are Asmachta. Even though the Rambam writes that one can be Makneh (transfer ownership of) Davar she'Lo Ba l'Olam (something net yet in the world) to Aniyim, that is because it is a vow and he must fulfill it. Even though the Kinyan was void, he intended to vow. Here, the person did not intend to transgress and pay the fine.

Rosh (Teshuvah 13:2): If Reuven was an Arev (guarantor) for Shimon, that if Shimon will not come to Beis Din at the proper time Reuven will give 1000 Zuz to Hekdesh, and Shimon did not come, R. Baruch ruled that Reuven must give. Even though it comes from Asmachta, Asmachta does not apply (here to exempt him). This is because Amirah l'Gavoha (saying 'I give this to Hekdesh') has all the power that a person can give to another (Rabbeinu Meir).

Teshuvas Rashba (attributed to the Ramban, 183): If one was Makdish through Asmachta, Hekdesh acquires. R. Baruch explains that Beis Shamai holds that the man said 'I will be a Nazir for the cow if it stands', i.e. if it fulfills it intent. Even though he expected to stand it up and not be a Nazir, he is a Nazir. Beis Hillel argue only because they hold that he stipulated about it standing (by itself or through him), but they would agree that he is a Nazir if his intent was like Beis Shamai say. R. Yehudah says that he made it a Korban, and we offer it.

Poskim

Shulchan Aruch (CM 207:19): A Neder, Shevu'ah or handshake helps even for Asmachta.

Source (Rabbeinu Meir (493-44), cited by Mordechai Bava Kama 44-46): A Neder, Shevu'ah or handshake helps even through Asmachta, for usually these are contingent. Yakov vowed "if Hash-m will be with me... (I will tithe what You give to me)", and Yisrael vowed "if You will give this nation into my hands (I will make the cities Cherem" - Bamidbar 21:2).

SMA (53): The Rivash (335) says that a Shevu'ah is no less than an esteemed Beis Din. According to R. Tam, there is never Asmachta in an esteemed Beis Din. However, some Ge'onim say that this is only if there was a Kinyan from now. If not, the Kinyan is void, and only the Shevu'ah obligates him. He can permit it, and if he died, his heirs are exempt.

Rebuttal (Bach 27 DH Kosav b'Mordechai): The one who asked the Rivash held that Shevu'ah helps like an esteemed Beis Din to remove Asmachta. The Rivash merely said that one can say so only according to R. Tam. He himself (341,344) explicitly says that the Kinyan is invalid in spite of the Shevu'ah. However, the Shevu'ah obligates him to pay, and we force him.

Bach (27 DH Nish'alti): If one obligated himself to fulfill a sale through a document, oath and a fine, if he pays the fine he need not fulfill the sale. Perhaps he intended that the fine will exempt him. The other party cannot prove otherwise. When there was only a Kinyan and a fine, the Rashba said that the fine does not exempt him. Here, the sale was based primarily on the fine, because a Shevu'ah can be permitted.

Shach (27): Mahara Sason (64) says that paying a fine does not exempt.

Rema: The same applies if he wrote in a document that he accepts a severe Cherem and Shevu'ah mid'Oraisa, just like an important Beis Din helps. This seems correct, even though some disagree.

Gra (62): It helps because it is an admission.

SMA (54): This is even if he did not accept it, just the document says that he did. We find that it helps to write 'we acquired in an esteemed Beis Din', even if it is known that they did not.

Rema: If one vowed to Tzedakah or Hekdesh through Asmachta, it acquires.

Source (Mordechai Bava Kama 44,46): Asmachta helps regarding Hekdesh, for Amirah l'Gavoha is like Mesirah l'Hedyot (handing it over to a person), i.e. in a way that Mesirah helps. Similarly, the command of a Shechiv Mera (one who fears lest he die from his illness) is as if a valid Mesirah was done, even though it is Asmachta. R. Shimshon says that even though one cannot be Makneh Davar she'Lo Ba l'Olam, since he can be Makneh it after it is in the world, an Amirah to Hekdesh now helps for when it comes to the world, for he must fulfill his vow. This is even though it is also Asmachta. R. Nesan'el says that Asmachta acquires mid'Oraisa. "Anochi E'ervenu" teaches that a guarantor is liable, even though it is Asmachta. Therefore, Asmachta works for Hekdesh and Tzedakah (Chachamim did not invalidate it).

Beis Yosef (DH u'Teshuvas): Hagahos Ashri (Sanhedrin 3:7) says that if something is Asmachta for regular people, it is Asmachta also for Aniyim. The Terumas ha'Deshen concluded like the Mordechai.

Shulchan Aruch (YD 258:10): If one vowed to Tzedakah through Asmachta, e.g. if I do this matter I will give this sum to Tzedakah, and he did it, he must give.

R. Yerucham (166a, cited in Beis Yosef DH u'Mihu): There are three laws. If he stipulated about Reshus (not a Mitzvah), e.g. if I will not go to the place Ploni I will fast or give Tzedakah, this is Asmachta (it is void). If he stipulated to make himself zealous to do a Mitzvah, e.g. if I will not do this Mitzvah I will fast or give Tzedakah, this is not Asmachta. If he stipulated to save himself from distress, e.g. "if Hash-m will be with me...", this is not Asmachta. Even the first category is not Asmachta if he obligated himself with a Kinyan in a document, for Amirah l'Gavoha has all the power that a person can have.

Shach (21): The same applies to all Nedarim, even not to Tzedakah. Asmachta does not apply to Nedarim (CM 207:19).

Taz (7): Regarding Tzedakah, Asmachta acquires. However, the Rivash (281) says that if one said 'if I jest, I will give this to the king and this to Hekdesh', since it is Asmachta regarding the king, it is Asmachta also regarding Hekdesh. If one said 'you and the donkey should acquire', even the man does not acquire.