Gemara

(Mishnah - Beis Shamai): If one said 'I am a Nazir from dried figs, he is a Nazir;

Beis Hillel say, he is not a Nazir;

Beis Shamai hold that 'I am a Nazir' accepts Nezirus. 'From dried figs' is an attempt to nullify his Nezirus through regret. Beis Shamai hold that one cannot permit a vow of Hekdesh. The same applies to Nezirus.

Beis Hillel hold like R. Shimon, who exempts one who vowed unlike the way people vow.

Nedarim 59a (R. Aba): Since one can permit his vow, a vow is like a Davar she'Yesh Lo Matirim (something permitted in another situation), which is not Batel in a majority of Heter.

Question: One can permit a declaration of Terumah, yet it can be Batel!

Answer: The case is, the Terumah was given to a Kohen, so the Yisrael may no longer permit his declaration of Terumah.

78a (Beraisa): Regarding vows, it mentions the heads of the Shevatim (to teach that a Chacham can permit by himself). This also applies to Shechutei Chutz (slaughtering a Korban outside the Mikdash).

(Rav Sheshes): This teaches that one may permit a vow of Hekdesh.

Beis Shamai do not learn the Gezeirah Shavah "Davar- Davar".

Avodah Zarah 13a (Beraisa): Nowadays (after the Churban), one should not be Makdish. If one was Makdish an animal, we lock it up so it will starve...

Rosh Hashanah 6a: "B'Ficha" teaches that Bal Te'acher applies to Tzedakah.

Rishonim

Rif and Rosh (Avodah Zarah 4a and 1:13) bring the Beraisa that if one was Makdish nowadays, we lock up an animal...

Hagahos Ashri: R. Tam says that if someone said 'Hekdesh', we prompt him to regret this by saying 'had you known that this forbids it to everyone and obligates burial, would you have called it Hekdesh?' If he says 'no', we permit it, for we hold that Yesh She'alah b'Hekdesh even retroactively after one benefited, all the more so for the future. This is when he intended to give this object to Tzedakah, but said 'Hekdesh'. If he intended for a different object, this is mistaken Hekdesh, and no She'alah is needed.

Rambam (Hilchos Nedarim 4:7): One may permit Nidrei Hekdesh just like one may permit Nedarim of Isur.

R. Betzalel Ashkenazi (Teshuvah 14 DH v'Nireh): In the case with Rav Yosef, the Rashba (in a Teshuvah) obligates Reuven only due to his Neder. If he were obligated due to a Kinyan (acquisition), he could not retract through Hataras Nedarim, for the poor already acquired. However, this is wrong. One can permit Hekdesh Mizbe'ach and Bedek ha'Bayis, even though Dibur (the words to Hekdesh) made a Kinyan! The Rashba himself (704) wrote that Dibur does not make a Kinyan in every respect. It merely eliminates the need for Mesirah. In Teshuvah 563 he said that that nowadays, one who is Makdish is like one who gives to the poor. He can retract unless someone acquired for them. However, in Teshuvah 656 he requires She'alah, for one who wants to retract from Hekdesh needs a Pesach and regret, like other Hataras Nedarim. If the money was given over, he cannot retract at all.

R. Betzalel Ashkenazi (ibid.): The Ran says that a Pesach is better than regret, for a Pesach makes the vow a mistake from the beginning. This helps even for Hekdesh, but regret from the beginning does not. Since it becomes Hekdesh right away, how can one regret a Mitzvah?! One can permit Hekdesh only because we hold that mistaken Hekdesh is invalid. This shows that a Pesach is required. The Rashba permits Hekdesh Aniyim through regret from the beginning. If it were totally as if it was given over, he would require a Pesach. Reuven had left and tarried long enough to permit his vow through a Chacham. This is why Rav Yosef needed to say that he already acquired for the Aniyim. If not, Reuven would have had a Migo. We would believe him to say 'I never meant to give it to Aniyim (I just alerted the judge to check if I deserve only this paltry amount that is embarrassing to take),' Migo that he could say that he permitted it through regret from the beginning. Nowadays, all Hekdesh is for Aniyim, and one is believed with other claims due to the Migo that he permitted it through regret. In Siman 656 the Rashba discusses when we know that he did not permit his vow, so there is no Migo. The Ro'oh holds that Hekdesh Aniyim is like proper Hekdesh and requires a Pesach, therefore there is no Migo.

Poskim

Rema (YD 258:1): One should not say 'this coin is for Hekdesh.' Rather, he should say 'for Tzedakah.' In any case, if he said 'for Hekdesh' Stam (without specifying), he meant Tzedakah for the poor.

Gra (3): In Galil we permit one who said 'Terumah' Stam, for there people are not familiar with (and do not regularly discuss) Terumas ha'Lishkah (Nedarim 18b). Nowadays, people are not familiar with Hekdesh Bedek ha'Bayis.

Rema (ibid.): If he says that he intended for real Hekdesh, it is forbidden to all. He must ask a Chacham. We permit him through regret, like other Nedarim.

Shulchan Aruch (6): One who vowed to Tzedakah cannot retract unless he asks a Chacham and the Chacham permits him. If it reached the Gabai (overseer of Tzedakah), he cannot permit it.

Beis Yosef (259 DH Kasuv Od): If a Shechiv Mera (one who fears lest he die from his illness) was Makdish his money or gave it to Aniyim, some say that it is like Safek Isur and he cannot retract. He should fulfill all opinions and permit his Hekdesh, for we hold that Yesh She'alah b'Hekdesh. However, after he gave to the Gizbar he cannot retract, just like one cannot permit Terumah after the Kohen received it.

Radvaz (4:134, cited in Pischei Teshuvah 8): We excommunicate a Chacham who permits the vow, for he causes a loss to Aniyim. B'Di'eved, it is permitted. Avi ha'Ezri says that we cannot force the Noder to give, for he can say that permitted it. I say that we ask him who permitted it. If that person denies it, we force the Noder to give. He is not believed to say that Ploni permitted his vow and went away, for we do not establish Ploni to be a Rasha. We force him to give to the first Oni who requests. I obligate one who decided in his heart to give, but we do not force him.

Maharlbach (4): All agree that one can permit Nidrei Hekdesh. Why can one regret Avodas Hash-m?! Even with regret one should permit them only due to dire straits. If one vowed to give a fine to Hekdesh if he permits a vow, it is easier to be lenient, for some say that Asmachta applies to Hekdesh. If it is a small fine, he should pay. If it is too much, he should permit it covertly, lest people permit vows to Hekdesh in other cases.