Gemara

(Rabah bar bar Chanah): There were two men. One ate his Korban Pesach for the sake of the Mitzvah, and the other ate it Achilah Gasah (stuffed himself). "Tzadikim will go in them" applies to the first man. "Resha'im will stumble in them" applies to the latter.

Objection (Reish Lakish): Why do you call the latter a Rasha? Granted, he didn't do the Mitzvah ideally, but he did fulfill it!

Yevamos 40a - Suggestion: A Beraisa permits eating the remainder of a Minchah (after Kemitzah) with appetite, or Achilah Gasah.

Rejection: The latter is not considered eating!

Yoma 80b (Reish Lakish): One who eats Achilah Gasah on Yom Kipur is exempt. "One who will not afflict himself" excludes one who harms himself.

(R. Yirmeyah): If a non-Kohen ate Terumah (b'Shogeg) Achilah Gasah, he pays principal, but not Chomesh. "When one will eat" excludes one who harms himself.

Bava Kama 110a (Rav Papa): If one is sick and can eat only with difficulty, this is like Achilah Gasah. We do not give Kodshim to such a Kohen, even if he offered them.

Bava Metzia 87b (Beraisa): A worker may eat "Sav'echa (to satiation)." He may not eat Achilah Gasah.

Rishonim

Rambam (Hilchos De'os 4:15): Achilah Gasah is like lethal poison for every person. It is the primary cause of all illnesses.

Rambam (5:1): A Chacham should eat only food good for his health, and not eat Achilah Gasah nor seek to fill his stomach.

Rosh (Teshuvah 22:4, cited in Beis Yosef OC 291): If the morning Seudah lasted until seven hours, the time for Minchah, my Rebbeyim would cease eating, bless, and immediately fulfill Seudah Shlishis. I do the same. If not, since the Seudah lasted so long, they would be able to eat Seudah Shlishis only Achilah Gasah. However, one cannot fulfill Seudah Shlishis before the time for Minchah. After the time for Minchah, interrupting the meal and blessing ha'Motzi again is not increasing Berachos without need, since he does so for the honor of Shabbos, to fulfill Seudah Shlishis. Some say that if one was eating on Erev Shabbos and Shabbos came, he blesses Birkas ha'Mazon, says Kidush and resumes eating. The same applies to splitting a meal to fulfill Seudah Shlishis.

Ran (Pesachim 23a DH Dilma): Achilah Gasah is not called eating, both for Mitzvos and for Isurim. One is exempt for eating Achilah Gasah on Yom Kipur or of Terumah. Achilah Gasah is when one already ate so much that now he can eat only with difficulty. Eating when one is already satiated, e.g. esteemed foods at the end (of a meal) is surely called eating. (This is more esteemed. This is why Pesach and Kodshim are eaten after satiation.) Matzah and Maror may be eaten either way (whether or not one is already satiated).

Tosfos (Pesachim 107b DH Dilma): Achilah Gasah is not eating, like it says in Yoma. However, we say that one was Yotzei Pesach! R. Tam says that there are two kinds of Achilah Gasah. If he loathes eating, he is exempt for Yom Kipur. If he has no appetite, but he tastes (the food, this is considered eating). Pesach is eaten (l'Chatchilah) when satiated, i.e. but he has a little appetite. Also, we can say that one who ate Korban Pesach Achilah Gasah fulfilled Pesach (i.e. he owned a share of a Korban Pesach, and he could have eaten it at night), even though he did not fulfill the Mitzvah of eating Pesach, for eating is not Me'akev.

Ri'az (in Shiltei ha'Giborim Berachos 35b Sof 2): If one is disgusted by food and his throat does not enjoy eating, he does not bless before or after.

Poskim

Shulchan Aruch (OC 291:3): If the Shabbos morning meal lasted until the time of Minchah, one interrupts his meal, say Birkas ha'Mazon, washes, blesses ha'Motzi and eats (the rest of his meal). This is proper. If not, since the meal lasted so long, later he would be able to eat only Achilah Gasah.

Beis Yosef (DH v'Chen): The Rosh (22:13) says that one should not teach this in public, for many do not know that one may not do so before midday,and many do not know this.

Note: The Rosh was asked if one may expound this in public. He answered that many are unaware that one may not fulfill Seudah Shlishis before midday. One could have understood this to mean that one may expound it, just he must warn people not to split the meal before midday!

Taz (2): As long as one is eating, the stomach is open. After the meal, it closes (so eating then is prone to be Achilah Gasah). It is good to interrupt in between with Divrei Torah or a short stroll.

Magen Avraham (6): One must get up and walk a little in between. Those who remain at the table are not Yotzei (Seudah Shlishis), for it is like one meal.

Mishnah Berurah (15): We are not concerned for causing an unnecessary Berachah, since he is forced to do so to fulfill Seudah Shlishis properly. The Rema (below) says that one who can eat after Minchah should do so, due to concern for unnecessary Berachos.

Note: Seemingly, the Rema just teaches that one should eat Seudah Shlishis after Minchah. If the concern is unnecessary Berachos, why does he say 'after praying Minchah?' He should forbid splitting the meal also if one could eat three or four hours later, before praying Minchah!

Rema: One who knows that he can eat after praying Minchah with the Tzibur may not fulfill Seudah Shlishis before Minchah. However, if he did, he was Yotzei.

Mishnah Berurah (16): I.e. he can eat after Minchah and it will not be Achilah Gasah.

Rema (476:1): One should not eat too much at the Seder, lest he eat the Afikoman Achilah Gasah.

Beis Yosef (DH Kosav): Eating the Afikoman should not be a toil. It says about one who eats Matzah Achilah Gasah "Resha'im will stumble in them."

Mishnah Berurah (6): Afikoman commemorates Korban Pesach. One should eat it when satiated, but he stil has some appetite. If he detested eating he was not Yotzei (see Shulchan Aruch 612:6 below).

Kaf ha'Chayim (17): There are three kinds of eating. For Mitzvos Aseh, the ideal Mitzvah is when he has appetite. If he has no appetite but he does not loathe eating, he fulfills the Mitzvah, but not ideally, and for Isurim he is liable. If he loathes eating, he was not Yotzei, and if he ate Isur he is liable.

Shulchan Aruch (612:6): If on Yom Kipur one ate Achilah Gasah, e.g. right after eating on Erev Yom Kipur, to the point that he detested the food, he is exempt.

Rema: If he ate spiced foods after eating (to satiation), he is liable, for one finds room for such food.

Bach (184:2 DH u'Mah): Some texts of the Tur say 'if one ate and went away, he may eat more and bless in the new place, as long as he is not satiated from what he already ate.' If he was satiated, he did not benefit from the latter eating, so it is not considered eating. This is wrong. As long as he is not disgusted by his food, it is called eating. It is no worse than Pesach and Afikoman, which are eaten when satiated.

Mishnah Berurah (197:28): If one was satiated before eating, and ate Achilah Gasah that he did not need, even so if his throat enjoyed eating, he blesses before and after and can be Motzi others.If he was disgusted by it and his throat did not enjoy, it is improper to bless before or after, for this is not considered eating for any Mitzvos of the Torah.

Bach (300:1): One should set his table on Erev Shabbos and Motza'ei Shabbos even if he needs only a k'Zayis, i.e. he is already satiated and whatever he eats is Achilah Gasah. He needs only a k'Zayis to fulfill the Mitzvah of Seudas Leil Shabbos or Melavah Malkah.

Mishnah Berurah (300:1): L'Chatchilah, one should eat bread for Melavah Malkah, with meat or cooked foods. If one is concerned for Achilah Gasah, e.g. in summer when Seudah Shlishis is late, he can fulfill Melavah Malkah with Mezonos or at least fruits.

Birkei Yosef (Shiyurei Berachah YD 238:1): If one swore to eat a loaf, and ate it Achilah Gasah, it is not clear whether he fulfilled his oath.