Gemara

43a (Mishnah): If Reuven was Mudar Hana'ah from Shimon and they were alone on the road, and Reuven has nothing to eat, Shimon leaves the food on a rock or on the fence and declares it Hefker (ownerless). Reuven may take it;

R. Yosi forbids this.

Question: Why does R. Yosi forbid?

Answer #1 (R. Yochanan): He holds that just like one may retract from a gift until the recipient gets it, one may retract from Hefker until someone takes it.

Answer #2 (Rava): R. Yosi decrees to forbid due to a gift like the case in Beis Choron. (Someone gave a 'gift' to evade the Isur of a Mudar Hana'ah, but he did not truly intend that it is a gift.)

44a (Beraisa #1): If Reuven declared his field to be Hefker, for three days he may retract, but not after this.

If he said 'this field should be Hefker for one day', or week, month, year or Shemitah cycle, he can retract only until someone acquires the field.

Question: The Reisha is like Chachamim, and the Seifa is like R. Yosi!

Answer #1 (Ula): Also the Seifa is like Chachamim. They agree that he can retract before someone acquired it. Hefker for a year or Shemitah cycle is different, for this is not common.

Answer #2 (Reish Lakish): Since the Seifa is like R. Yosi, also the Reisha is like R. Yosi. He can retract only for three days, lest the law of Hefker be forgotten.

Question: If so, even the first day, he should not be able to retract!

Answer (Rabah): Chachamim enacted that he can retract due to swindlers (who (insincerely) say that their fields are Hefker to exempt them from tithes. Through the enactment, it is not Hefker, and tithes must be taken.

Question (Beraisa #2): If one made his vineyard Hefker and promptly harvested it, he must leave Leket, Shichchah and Pe'ah (gifts for the poor). He is exempt from Ma'aser.

Ula holds that Beraisa #2 is like Chachamim. Mid'Oraisa, the vineyard is Hefker. According to Reish Lakish, why is it exempt from Ma'aser?

Answer #1: Reish Lakish explained Beraisa #1 like R. Yosi. He admits that Beraisa #2 is like Chachamim.

Answer #2: In Beraisa #2, he made it Hefker in front of three people. R. Yosi considers this to be proper Hefker. In Beraisa #1, Hefker was done in front of two (or less). This is not Hefker mid'Oraisa.

(R. Yochanan): Hefker in front of three is Hefker. In front of two it is not Hefker.

(R. Yehoshua ben Levi): Mid'Oraisa, even in front of one person it is Hefker. Chachamim said that it should be done in front of three, in order that one could acquire it and the other two could testify to this.

Shabbos 18a: Beis Shamai require Shevisas Kelim (one must allow his vessels to rest on Shabbos).

Question: Why do Beis Shamai permit (to leave from before Shabbos) beer brewing in a barrel, oil burning in a lamp, food in a pot on a fire, and the Korban Pesach on a spit?

Answer: Beis Shamai hold that he makes these Kelim Hefker.

Rishonim

Rif: If Reuven declared his field to be Hefker, for three days he may retract. After this, he cannot retract.

Rambam (Hilchos Nedarim 2:17): If Reuven declared his field to be Hefker, and no one acquired it, for three days Reuven can retract. After three days he cannot retract, unless he acquired it first. He or anyone else is like one who acquired from Hefker.

Kesef Mishneh: The Rambam holds like the Rosh (below), that within three days someone else can acquire it before Reuven retracts. This is unlike the Ran (43b DH Tanya). The Rambam's words connote that he can retract after three days if he acquired it first. Really, he means that if he retracts within three days, it is as if it was not Hefker, so he must tithe it. If he acquires after three days, it is as if he acquired from Hefker, so it is exempt from Ma'aser.

Rambam (18): If one said 'this field should be Hefker for one day', or week, month, year or Shemitah cycle, he can retract only until he or someone acquires the field, but not afterwards. He can retract before anyone acquired it is because this is unusual. People do not normally make Hefker for a limited time.

Kesef Mishneh: This is like the Ran, who says that Ula's answer is primary.

Radvaz: Hefker for a day or week is common! Rather, Chachamim did not distinguish. If he was not Mafkir it totally, he wants it to remain his until someone takes it, therefore it is not exempt from Ma'aser.

Perush ha'Rosh (43b DH Kol): Within three days, he or another can acquire from Hefker, and the owner cannot retract. Since he can retract before someone acquires, it is not considered Hefker until someone acquires it.

Poskim

Shulchan Aruch (CM 273:9): If Reuven declared his field to be Hefker, and no one acquired it, for three days Reuven can retract. After three days he cannot retract. If he acquired it (before anyone else), he is like one who acquired from Hefker.

Nesivos ha'Mishpat (2): If he re-acquires his field within three days, this is like retraction. The exemption from Hefker is only when he leaves the field Hefker, and merely takes the produce. A swindler fears to do so, lest someone else take fruits from another part of the field.

Shulchan Aruch (10): If one said 'this field should be Hefker for one day', or week, month, year or Shemitah cycle, he can retract only until he or someone acquires the field, but not afterwards.

SMA (14): If he or anyone else acquired from Hefker, it is exempt from Ma'aser, even though the Hefker was limited. We learn from Shemitah, which is Hefker only for a year.

Rema (OC 246:3): (If one lent his animal to a Nochri and it will not returned before Shabbos,) if he wants, he can be Mafkir it in front of three people, like other Hefker. No one can acquire it, for surely he only wants to avoid the Isur Shabbos.

Beis Yosef (DH v'Nir'eh): He specifies that it is Hefker only for Shabbos, for then it is rented to the Nochri, so no one else can acquire it. After Shabbos, it is as if he retracts and acquires it. A limited Hefker is valid, like it says in Nedarim.

Shulchan Aruch ha'Rav (9, cited in Kaf ha'Chayim 52): No one else can acquire it on Shabbos, for the owner makes it Hefker only when the Nochri uses it on Shabbos. The Nochri will not allow another to take it then, and even if he did, it is idle from the Nochri's work and reverts to the owner.

Kaf ha'Chayim (46): A Chacham permitted one who sold tobacco through Nochrim to be Mafkir it before Shabbos. The Chasam Sofer (63) disagreed. The Heter of Hefker was for Shevisas Behemto, not for Melachah, and only when the animal is outside the Yisrael's Reshus. Mar'is ha'Ayin is also a problem.