Gemara

Question: If someone did not make an Eruv Tavshilin, surely he is forbidden (to cook). Is his food forbidden?

If it is forbidden, others may not cook his food unless he transfers ownership of it to them.

Answer - Beraisa: If someone did not make an Eruv Tavshilin, he may not cook (or bake or do Hatmanah) for himself or for others, and others may not cook for him. If he transfers ownership of his food to them, it is permitted.

This shows that he and his food are forbidden.

Question: If someone transgressed and baked (without an Eruv Tavshilin), what is the law?

17b - Answer (Beraisa): One may eat his Eruv Tavshilin. If he ate it before cooking (or baking...), he may not cook for himself or for others, and others may not cook for him. He may cook for Yom Tov, and if there are leftovers he may have them on Shabbos. He may not scheme (and intentionally cook extra for Shabbos). If he schemed, it is forbidden.

Rejection #1 (Rav Ashi): We are more stringent about one who schemed than about one who simply transgressed.

Rejection #2 (Rav Nachman bar Yitzchak): The Beraisa is Beis Shamai according to Chananyah (who says that the Heterim to cook, bake and do Hatmanah are only for one who made bread, a Tavshil, and did Hatmanah, respectively. Just like he is more stringent about Eruv Techumim, he is more stringent about scheming.)

(Mishnah): If he ate or lost the Eruv, he may not rely on it to cook.

Abaye: The Halachah is that if the Eruv was eaten after he began kneading, he may finish.

21b - Mishnah: R. Gamliel was stringent not to do Hatmanah on Yom Tov for Shabbos, like Beis Shamai.

Question: If he made Eruv Tavshilin, Beis Shamai should permit even Hatmanah. If he did not make an Eruv, even Beis Hillel should forbid!

Answer: #1 (Rav Huna). He did not make an Eruv. He is permitted only Kedei Chayav (the basic life essentials).

Rav Huna: If someone did not make an Eruv Tavshilin, we bake one loaf for him, cook one Tavshil for him, and light a Ner for him.

R. Yitzchak: We also roast a small fish for him.

Support (Beraisa): For one who did not make an Eruv we bake one loaf, do Hatmanah on one Tavshil, light a Ner and heat one flask of water;

Some say, we also roast a small fish for him.

Rishonim

Rif and Rosh (2:10): If someone did not make Eruv Tavshilin, he and his food are forbidden.

Ran (DH Ibo'i): He must give his food to another (to permit cooking it) and say that it is a gift. He does not use Chalifin, rather, Meshichah.

Question: If his food is forbidden, it should be forbidden also to others, just like regarding Techumim (37a)!

Answer #1 (Ran, ibid.): Techumim are determined Bein ha'Shemashos. The Heter to cook for Shabbos depends on the existence of the Eruv. If it is lost or eaten, the Heter ceases. Therefore, the food is permitted if its current owner has an Eruv.

Answer #2 (BaHaG, brought in Ran, ibid.): Indeed, from the Heter for others to cook his food we prove that his food is not forbidden!

Rif: The Gemara did not resolve the question about one who did not make Eruv Tavshilin and cooked. Perhaps we are more stringent about one who schemed than about one who transgressed b'Mezid.

Rif: If the Eruv was eaten after he began kneading, he may finish (and bake the bread).

Rambam (Hilchos Yom Tov 6:5): If the Eruv was eaten, lost or burned, he may cook only what he intends to eat on Yom Tov. If the Eruv was eaten after he began kneading, he may finish.

Ra'avad: If he cooked but did not bake, or vice-versa, and the Eruv was eaten, he may keep the prepared food for Shabbos.

Magid Mishnah: Even if the food was intended for Yom Tov, he may save it for Shabbos and cook more for Yom Tov.

Rambam (9): If someone was not Me'arev and no one was Me'arev for him, just like he may not cook or bake, others may not cook or bake his food. If he transfers ownership of his food to them, it is permitted. The receiver may later give back the food as a gift.

Magid Mishnah: The Rambam does not bring the Heter for one loaf, Tavshil and Ner because he holds that the Halachah does not follow that opinion.

Rambam (10): If someone who was not Me'arev cooked or baked for Yom Tov and there were leftovers, or if he invited guests and they did not come, he may eat what remains on Shabbos. If he schemed, it is forbidden. If he transgressed and cooked it is permitted.

Magid Mishnah: The Gemara did not resolve this. It is a Safek mid'Rabanan, so we are lenient.

Rambam (ibid.): We are more stringent about one who schemes, because if he will be permitted everyone will scheme and Eruv Tavshilin will be forgotten. It is uncommon for someone to transgress b'Mezid. If he transgressed today, he will not do so another time.

Rosh (2:10): The Gemara did not resolve the question about one who did not make Eruv Tavshilin and cooked. Rav Ashi and Rav Nachman bar Yitzchak are Amora'im Basrai, and they rejected the proof that it is forbidden. This shows that they permit. Presumably, for the sake of Kavod Shabbos Chachamim did not fine the person.

Rosh (2:12): If the Eruv was eaten after he began kneading, he may finish. Perhaps he may finish only the dough. Or, perhaps he may finish all the needs of Shabbos; Abaye merely mentioned the first preparation.

Rosh (2:16): Some infer that (if Reuven did not make an Eruv) Ofin (we bake) one loaf for him..., i.e. Reuven himself may not cook. This is wrong. If there is someone else there (Shimon) who (made an Eruv and) may cook, Reuven could give all of his food to Shimon, and Shimon could cook everything! Why did Chachamim need to permit Kedei Chayav? Rather, there is no one there who made an Eruv. Reuven's household may bake and cook for him Kedei Chayav. The Yerushalmi supports this.

Rosh (ibid.): Reuven is allowed to light (one) Ner. This implies that Eruv Tavshilin is required to light Neros for Shabbos. In the text of Eruv Tavshilin we say '(this Eruv permits us to bake, cook, light and do Hatmanah'.

Poskim

Shulchan Aruch (OC 527:17): If the Eruv was eaten after he began kneading, he may finish the dough (and bake it). Similarly, if it was eaten after he began cooking, he may finish the Tavshil.

Magen Avraham (16): If he cut vegetables this is the start, even before putting the pot on the fire. This is analogous to one who began kneading.

Shulchan Aruch (18): If he cooked but did not bake, or vice-versa, and the Eruv was eaten, he may keep the prepared food for Shabbos and cook more for Yom Tov. This is even if he prepared it for Yom Tov.

Magen Avraham (17): It is forbidden to leave the food for a Yom Chol and cook more for Yom Tov.

Shulchan Aruch (19): If one did not make an Eruv he may light Ner Shabbos. Some forbid.

Beis Yosef (DH Mi): The Rambam's text of Eruv Tavshilin does not mention lighting Neros. He holds that an Eruv is not needed to permit this.

Bach (DH Mi): B'Di'eved, one may rely on the Rif and Rambam for the Mitzvah of Neros Shabbos.

Rebuttal (Magen Avraham 18): The Rif and Rambam only mentioned the primary Melachos, but they agree that an Eruv is needed to permit lighting. All permit lighting one Ner; this fulfills the primary Mitzvah of Ner Shabbos.

Mishnah Berurah (55): One should give the Neros to others to light them, or light only one Ner.

Kaf ha'Chayim (113): One who makes an Eruv just for lighting should not bless on it, since it is a Safek whether or not it is necessary.

Shulchan Aruch (20): If one did not make an Eruv, just like he may not cook for himself, he may not cook for others, and others may not cook for him.

Mishnah Berurah (56): If a man made an Eruv, his household is permitted even if he did not Mezakeh for them.

Beis Yosef (DH u'Mah she'Chosav Al): Ba'al ha'Itur permits him to cook for others (who made an Eruv). He is like their Shali'ach, and is like the Meshale'ach. However, the Beraisa and Rambam connote that it is forbidden.

Shulchan Aruch (ibid.): The only solution is for him to give his flour and food to others as a gift, and they bake and cook and give to him. This is permitted even in his house.

Kaf ha'Chayim (117,118): We do not do Chalifin because it looks like business. They must take the food to their Reshus or lift it a Tefach.

Shulchan Aruch (ibid.): If there is no one there who made an Eruv, some permit him to bake a minimal loaf, cook one Tavshil and light one Ner.

Kaf ha'Chayim (119,121): Some say that if there are others, he himself may not cook. In any case it is better to give his food to them so he will have Lechem Mishneh. He himself may make one loaf and one Tavshil as big as needed for all of Shabbos.

Rema: If one left an Eruv but did not mention which Melachos it permits, rather, he said 'this permits to do all needs of Shabbos', it is as if he did not make an Eruv at all.

Mishnah Berurah (63): This is l'Chatchilah. If one did not detail Melachos, he should do so before Yom Tov. If he did not, he should give his food to others. If this is not possible, he may rely on those who do not require detailing Melachos.