Peah, Chapter 4, Mishnah 9. The Mishnah opens with the case of someone who gathered peah and wished to acquire it on behalf of another person:
"Mi shelikeit es hapei'ah ve'amar harei zu le'ish peloni ani" - a person harvested peah, and he himself is not poor but wealthy, so that the peah is not fit for him at all. He harvests it and declares that he wants it to enter the ownership of a particular poor man who is entitled to peah, and that he is acquiring it on that man's behalf.
"Rabbi Eliezer omer zachah lo" - the wealthy man does acquire the peah for that specific poor man, and no other poor person may take it any longer.
"Vachachamim omrim" - the Sages disagree: the poor man he had in mind does not become its owner on the strength of his statement alone, and therefore it is given to whichever poor person comes along, to the first one on the scene.
The basis of the dispute - the principle of 'migo':
The dispute rests on the well known concept of 'migo', familiar from many places in Shas. 'Migo' in Aramaic means 'out of' - out of the logic itself: from one ability that a person has, we derive a further ability.
According to Rabbi Eliezer there are two stages here:
The first migo: since the wealthy man could have declared all his property ownerless, giving away everything he has and becoming poor, he therefore has the ability to acquire the peah for himself.
The second migo: and since he himself is able to acquire the peah, he is also able to acquire it on behalf of another person.
The Sages say: we apply only a single migo, one line of reasoning alone. One may argue "I could have acquired it myself", but we do not combine two migos one on top of the other.
Leket, shichechah and peah of a non-Jew:
From here the Mishnah moves to an entirely different law, concerning three of the gifts to the poor: leket - what falls during the harvesting; shichechah - what is forgotten in the field; and peah - the corner of the field.
"Leket shichechah ufei'ah shel nochri chayav bema'asros" - ordinarily leket, shichechah and peah are exempt from tithes. However, a non-Jew is not obligated in the gifts to the poor, and therefore his produce is not considered leket, shichechah and peah, and his produce is obligated in Terumah and tithes. The mere declaration that part of his crop is leket, shichechah and peah does not remove the obligation of tithing.
"Ela im kein hifkir" - if he went through the formal process of hefker and made them completely ownerless, then the law that ownerless produce is exempt from Terumah and tithes comes into play.
The view of the Mishnah - two explanations:
The Rambam: the Mishnah was taught according to the view of Rabbi Meir throughout Shas, that a non-Jew's acquisition in Eretz Yisrael does not take effect to remove the obligation of tithes. A non-Jew's ownership in Eretz Yisrael is not sufficient to exempt his produce from tithing, and therefore it remains obligated. For if that were not so, the non-Jew himself would not have been obligated in tithes at all.
Others: there is no need to establish the Mishnah as following Rabbi Meir, since one can say that this is not a Torah obligation but a rabbinic one - it was the Sages who determined that a non-Jew's produce is obligated in tithes.
In summary: in this Mishnah we learned the dispute between Rabbi Eliezer and the Sages regarding one who gathered peah on behalf of a particular poor man, and its basis in the principle of 'migo' - whether we apply two migos (since he could have declared his property ownerless and acquired it for himself, he can acquire it for another as well) or only a single migo. We also learned that the leket, shichechah and peah of a non-Jew are obligated in tithes, since the laws of gifts to the poor do not apply to him, unless he declared them ownerless, along with the two explanations for the basis of this obligation - either following Rabbi Meir that a non-Jew's acquisition does not take effect in Eretz Yisrael, or as a rabbinic obligation.