Gemara

(R. Aba): On Shabbos one must cut (i.e. bless) on two loaves, to fulfill "Lechem Mishneh."

Rav Ashi: I saw Rav Kahana hold two loaves and cut one.

Pesachim 105a (Rav Amram): Rav said that Shabbos is not Kove'a regarding Havdalah. (One may continue eating on Motza'ei Shabbos without saying Havdalah.)

The Heter applies only to eating [or eating and drinking], but not to [only] drinking.

The Isur to continue drinking applies only to wine and beer, but not to water.

Kesuvos 64b Mishnah): One who feeds his wife through an intermediary must supply at least two Kabim of wheat every week:

Question: This is enough for 16 meals!

Answer: Our Mishnah is like R. Chidka, who obligates eating four meals on Shabbos. Alternatively, the extra meal is for guests.

Rishonim

Rambam (Hilchos Shabbos 29:10): It is a Mitzvah to bless on wine on Shabbos day before the second meal.

Rambam (30:9): One is obligated to eat three Shabbos meals, one at night, one in the morning and one at the time of Minchah. One must fix all three meals on wine and bless on two full loaves. The same applies to Yom Tov.

Ran (44a DH v'Chosav): R. Tam says that women are obligated to eat three meals and bless on two loaves, for the miracle of the manna applied also to them. He did not need to give this reasoning. We learn from "Zachor" and "Shamor" that whoever must guard Shabbos (not do Melachah) must remember it (say Kidush). This includes all obligations of Shabbos.

Beis Yosef (OC 291 DH Kasvu): Shibolei ha'Leket says that "Ichluhu ha'Yom" applies to men and women alike. It is clear from Kesuvos 64b that women are obligated in Seudah Shlishis.

Question: If someone did not fulfill Seudah Shlishis before the 10th hour on Erev Yom Tov, does the Torah Mitzvah of Seudah Shlishis override the mid'Rabanan Mitzvah to refrain, in order to eat the Yom Tov meal with appetite?

Answer (Maharil 94:2): Also Seudah Shlishis is mid'Rabanan. The verse is a mere Asmachta. A proof is from R. Tam, who obligates women in Seudah Shlishis because the miracle applied also to them. This reasoning is only for Mitzvos mid'Rabanan such as Megilah, Ner Chanukah and the four cups of wine. If it were even for Torah Mitzvos, this reasoning should obligate women in Sukah and Matzah! (They are obligated in Matzah, but we needed a verse to teach that.) I say that one should eat a k'Zayis of bread. This is better than fulfilling the meal with Targima, i.e. cooked foods. Also, the custom is that people do not eat on Motza'ei Shabbos until a while after dark, for the meal is not ready.

Poskim

Shulchan Aruch (OC 291:4): One need not say Kidush at Seudah Shlishis. However, one must [bless and] cut on two loaves.

Rema: If one eats many times during Shabbos, he must have two loaves at each meal.

Beis Yosef (DH v'Chosav): Many do not require Kidush at Seudah Shlishis, i.e. R. Yerucham citing the Ramah, the Mordechai, Teshuvas (Rashba, attributed to the) Ramban 210 citing Rabbeinu Meir, R. Yonah and Shibolei ha'Leket. Perhaps the Rambam does not require Kidush. Perhaps 'fixes the meal on wine' means that he drinks wine at the Seudah. Since all Poskim do not require Kidush, and perhaps even the Rambam does not require it, we do not make Kidush. One who makes Kidush does not lose, for perhaps the Rambam requires it, and the other Poskim do not forbid.

Bedek ha'Bayis: In Perek 29, the Rambam says that it is a Mitzvah to bless on wine before the second meal. This connotes that there is no Mitzvah before the third meal. If one does so, we do not protest.

Magen Avraham (9): Tikunei Shabbos says to bless on wine.

Mishnah Berurah (18): The day is equated to the night. Just like one Kidush suffices for the night, also for the day. Therefore, Chachamim enacted only one Kidush during the day. Regarding two loaves, all the meals are the same.

Kaf ha'Chayim (22): The Ari Zal says that Kidush does not apply, but one must bless on wine during the meal.

Rema (ibid.): He should have at least one whole loaf at Seudah Shlishis. From here came the custom to be lenient to be Botze'a (cut, and bless) on one whole loaf for Seudah Shlishis.

Beis Yosef (DH ul'Inyan): Shibolei ha'Leket says that one need not bless on two loaves at Seudah Shlishis. The verse discusses "Lechem Mishneh"; in the Midbar. After eating Shabbos morning, an extra portion did not remain at the time of Minchah! One who is careful about this will be rewarded. Hagahos Maimoniyos (30:9), the Mordechai and R. Yerucham say that it is obligatory. The Mechilta requires at least one full loaf.

Taz (4): On Erev Shabbos, two portions (each an Omer) fell for everyone. They made two loaves from each Omer. They ate one on Erev Shabbos, one on Shabbos night, one in the morning, so one loaf remained for Seudah Shlishis.

Mishnah Berurah (20): If one does not have a whole loaf, a piece the size of an egg suffices. Even though he does not fulfill the Mitzvah of Lechem Mishneh, he fulfills Mitzvas Seudah Shlishis.

Bi'ur Halachah (DH u'Lefachos): If one has one whole loaf and a piece, surely he cuts the loaf and leaves the piece for Melaveh Malkah. Even though Melaveh Malkah is a Mitzvah, Seudah Shlishis is far more important. Some people think oppositely. They err.

Rema (ibid.): However, one should be stringent to take two.

Gra (DH Aval): Shabbos 117b connotes like this. On Shabbos one needs two loaves for Betzi'ah, but not due to the meal.

Mishnah Berurah (21): It is proper to do so, for the first opinion is primary. It is good to bless on wine during the meal to do the ideal Mitzvah. If there is not Lechem Mishneh for all at the meal, the Botze'a should intend to be Motzi them with ha'Motzi. He tells them to intend to be Yotzei through his Berachah, so they will fulfill Lechem Mishneh.

Kaf ha'Chayim (26): One who is Motzi others says 'bi'Rshus Rabosai', even if he is the Ba'al ha'Bayis or the greatest one there. This is for humility.

Kaf ha'Chayim (23): The Ari Zal requires 12 loaves on the table for all the meals.

Shulchan Aruch (5): Seudah Shlishis must be with bread. Some allow using any food from the five grains.

Mishnah Berurah (24): The second opinion requires food from grain on which we bless Borei Minei Mezonos. The reason for the lenient opinions is because this meal is not normally eaten with appetite.

Mishnah Berurah (22,23): L'Chatchilah, one should have delicacies according to his ability also for Seudah Shlishis. All agree that l'Chatchilah one should have bread (Sa'if 4). They argue about b'Di'eved.

Kaf ha'Chayim (29): One should eat fish at Seudah Shlishis. It is nice to have eggs, for a sign of mourning over Moshe Rabbeinu (who died Shabbos afternoon).

Kaf ha'Chayim (30): It is proper to have bread even when Shabbos is Erev Yom Tov.

Shulchan Aruch (ibid.): Some allow accompaniments for bread such as meat and fish, but not fruits. Some allow even fruits.

Eshel Avraham (Butshats): Devar Moshe (1 OC 25:6) says that this is only if the fruits were cooked.

Shulchan Aruch (ibid.): The first opinion is primary, that one must use bread, unless he is too full.

Rema: Or, (one has Targima or fruits...) when one cannot use bread, e.g. when Erev Pesach is on Shabbos, so one cannot eat bread after Minchah.

Mishnah Berurah (25): Therefore, he should fulfill Seudah Shlishis through fried Matzah meal, meat and fish, or fruits.

Shulchan Aruch (6): Women are obligated in Seudah Shlishis.

Eshel Avraham (325:11): Even if one has no food to eat, he may not command a Nochri to cook or bake for him, even though it is a Torah Mitzvah for men and women to eat bread on Shabbos. The Magen Avraham (586:23) says that the Aseh of Shofar does not override Shevus, for it was enacted like Torah law, and an Aseh does not override the Lav and Aseh of Melachah on Yom Tov. Do not say that a woman may command, for she has no Isur Aseh of Melachah on Shabbos. This is wrong. Women are totally commanded about Shabbos (Magen Avraham 291:11). Also, if she would command, the Aseh [of eating bread] would not be fulfilled at the time the Lav is transgressed.

Aruch ha'Shulchan (1): Even if Seudah Shlishis is not a Torah Mitzvah, Moshe enacted it, for he received this from Sinai. They received manna for three meals, like the Tur brings from the Mechilta.