Gemara

104b (Mishnah): If he said 'Alai Minchah', he may bring any Minchas Nedavah;

R. Yehudah obligates bringing Soles, the choice Minchah.

105a: R. Yehudah requires Minchas Soles because it does not have a Shem Levai (accompanying name. The Torah calls it just "Minchah". The others have an added name, e.g. 'Minchas Machavas', 'Minchas Ma'afe Tanur'...)

Nedarim 52a (Mishnah): If one vowed from milk, he may have Kum (water that separates from the milk during curdling);

R. Yosi forbids.

52b: They do not argue. Each discusses his locale;

In Chachamim's region, milk is called milk, and Kum is called Kum. In R. Yosi's region, Kum is also called Kum of milk.

53a (Mishnah) If one vowed from dates, he may eat date honey. If one vowed from Stavaniyos (bad grapes that do not ripen), he may have vinegar made from such grapes;

R. Yehudah ben Beseirah says, one who vowed from a food is forbidden any 1. derivative called by the name of that food;

Chachamim permit.

Chachamim and the first Tana argue about R. Shimon ben Elazar's distinction;

(Beraisa - R. Shimon ben Elazar): If one vowed from any food that is normal to eat it, and it is normal to eat a derivative of it, such as dates and date honey, (even) its derivative is forbidden;

If one vowed from the derivative, (also) the food is forbidden;

If one vowed from a food that is not normally eaten, and it is normal to eat a derivative of it (e.g. vinegar of Stavaniyos), only the derivative is forbidden, for this was his intention.

53a (Mishnah): If one vowed from wine, he may drink apple wine. If one vowed from oil, honey or vinegar, he may have sesame (seed) oil, date honey and vinegar of bad grapes.

If one vowed from leeks, he may eat he may eat Kaplutos (large leeks). If one vowed from Yerakos (vegetables in which we eat the plant itself, not just the seeds) he may eat Yerakos of the field;

All these are permitted because they have a Shem Levai.

Rishonim

Rambam (Hilchos Nedarim 9:8): If one vowed from milk, Kum is permitted. If one who vowed from Kum, milk is permitted.

Rambam (14): If one vowed from wine, he may drink apple wine. If one vowed from oil, honey or vinegar, he may have sesame (seed) oil, date honey and vinegar of bad grapes. If one vowed from Yerek, Yerakos of the field are permitted, because all of these have Shem Levai, and he vowed only from something without a Shem Levai in that place. The same applies to all similar cases.

Rosh (Nedarim 6:3): The Yerushalmi says that R. Yosi forbids Kum to one who vowed from milk, because it is called by the name of its source. He would forbid cooked wine to one who vowed from wine, for it is called cooked wine. The Bavli says that R. Yosi and Rabanan each discuss their own regions. In Rabanan's region, milk is called milk, and Kum is called Kum. In R. Yosi's region, also Kum is called Kum of milk. If so, even Rabanan would forbid cooked wine to one who vowed from wine, for it is called cooked wine. Even though R. Yehudah ben Beseirah forbids anything called by the name of its derivative, and even what comes from it, and Rabanan argue, that refers to a food called by the name of its derivative. A food called by the name of its source is different. The Yerushalmi explains like this.

Lechem Mishneh (14): The Rosh forbids cooked wine to one who vowed from wine, even though it is called by a Shem Levai. This is unlike vinegar of Stavaniyos, for here the name of the source (Yayin) is first, which is primary, and afterwards we add the Shem Levai (Mevushal). Regarding vinegar of Stavaniyos, vinegar is the derivative, and it is primary and first. The Beis Yosef explained the Rosh this way. This is difficult, for Rabanan agree that a vow from milk forbids Kum, even though the name of the derivative is first and primary! This is not difficult for the Yerushalmi. It holds (6:4) that Kum is the whey (what congeals, like the Ra'avad on Halachah 8), and it is called by the name of milk (Chalav Maktera). However, this is difficult for the Bavli, and it seems that the Rosh explains the Bavli! Perhaps he holds that Kum is not a changed form, like the Ran says. The Rosh did not explain this; he relied on the reader to understand.

Ran (53a DH Gemara): The Ramban holds that the first Tana always forbids the food and permits the derivative. R. Shimon ben Elazar forbids the food and/or the derivative, whichever is normally eaten. R. Yehudah ben Beseirah agrees, but he also forbids the food even if it is not normally eaten. The latter Chachamim in the Mishnah hold like R. Shimon ben Elazar, and permit the food in a case when it is not normally eaten.

Ran (53a DH Asur b'Yerakos): One who vowed from Yerek is forbidden garden vegetables, for these are Stam vegetables. He is permitted field vegetables, for it has a Shem Levai. However, one who vowed from wine is forbidden cooked wine. The Ramban says that this is unlike field vegetables, which is a different species. Wine and cooked wine are the same species, even if it was cooked.

Ran (51b Min ha'Kum and 52b DH Gemara u'Rminuhu): A Beraisa teaches that if one vowed from Kum, R. Yosi forbids milk. Granted, one who vowed from milk may not drink Kum, for it is still has the name milk, for it is called Kum of milk. However, if one vowed from Kum, why is milk forbidden? It is not called milk of Kum! We can say that since Kum is called Kum of milk, they are one matter.

Rebuttal (Beis Yosef YD 217 DH ha'Noder): I did not find a Beraisa that says that if one vowed from Kum, R. Yosi forbids milk. It seems that the Tur's text of the Gemara did not have the Beraisa, so he permits milk Stam to one who vowed from Kum, i.e. even where Kum is called Kum of milk. The Mishnah connotes like this. The Rambam Stam permits Kum to one who vowed from milk, without distinguishing between places. This is astounding. The Gemara says that the first Tana forbids where Kum is called Kum of milk! Perhaps it is because the Yerushalmi connotes that R. Yosi and the first Tana argue. He holds that since it is possible to say that the Bavli agrees, we use all means to avoid an argument between the Bavli and Yerushalmi. I.e. the Gemara did not need to say that in Rabanan's region, they call milk milk and Kum Kum. It said so only for parallel structure, since it needed to say that in R. Yosi's region, they call Kum Kum of milk. Really, Rabanan permit in any place. Alternatively, since Kum is called a new name that milk is not called, it is permitted, even though it also is called by the name of milk. However, this is difficult, for the Gemara said that they do not argue, and each discusses his locale. Rather, the Rambam tries to equate the Bavli to the Yerushalmi. The Gemara had asked a contradiction in Rabanan, and to answer it, it suggested that Rabanan do not argue with R. Yosi. Really, they argue.

Ran (53a DH ul'Inyan): The Halachah follows the first Tana. If one vowed from dates or Stavaniyos, he is permitted their honey or vinegar.

Poskim

Shulchan Aruch (YD 217:12): One who vowed from milk is permitted Kum. One who vowed from Kum is permitted milk.

Gra (18): The Rambam and Shulchan Aruch do not distinguish between different places. Seemingly, they hold that the Sugya is like R. Yehudah ben Beseirah, but the Yerushalmi distinguishes. The Rambam often relies on the Yerushalmi.

Rema: Some say that if Kum is called by the name of milk, e.g. Kum of milk, it is forbidden.

Shach (17): This connotes that in such places, whether one who vowed from milk or Kum, both are forbidden. This is like the Ran; the Rema (Krakow edition) cites this from the Beis Yosef from the Ran. This is difficult, for the Beis Yosef solidly rejected the Ran! The Tur and Rashi and others are unlike the Ran! Also the Bach and Prishah (21) are unlike the Ran. Rather, the Rema discusses only one who vowed from milk. One who vowed from Kum is permitted milk in every place.

Shulchan Aruch (13): One who vowed from dates is permitted date honey.

Gra (19): This is like the first Tana. See the Ran (53a DH ul'Inyan).

Shach (19): One who vowed from 'these olives or grapes' is forbidden what comes from them. The Bach asked why the Tana did not teach similarly about dates. This is not difficult. The Tana is not a peddler. He need not teach every case. He taught about olives and grapes, and the same applies to everything!

Rema: Even though it is called by the name of dates, i.e. date honey, since it changed from its initial form, it is permitted. This is unlike Kum of milk. Also, it is called date honey only to distinguish it from other honey.

Taz (17): The Beis Yosef brought this answer from the Ran. R. Leiv of Prague says that Kum of milk is different, for it is still a liquid. Date honey was a solid and it became a liquid.

Shach (20): The Bach explains that Kum of milk is called so because it is still considered milk. This is not to distinguish it from other Kum, for nothing else is called Kum.

Gra (20): The Yerushalmi says that R. Yosi forbids something called by the name of its source. He argues with R. Yehudah ben Beseirah's law, who forbids something called by the name of its derivative. However, R. Yehudah ben Beseirah would agree to the law of R. Yosi.

Shulchan Aruch (ibid.): One who vowed from date honey may eat dates.

Gra (21): This is unlike R. Yehudah ben Beseirah.

Shulchan Aruch (ibid.): One who vowed from Stavaniyos is permitted vinegar that comes from them.

Shulchan Aruch (14): If one vowed from honey, he may eat date honey. If one vowed from vinegar, he is permitted vinegar of Stavaniyos.

Taz (19): Stam honey is of bees.

Shulchan Aruch (YD 217:15): If one vowed from wine, he may drink apple wine, but not cooked wine. If one vowed from oil, honey or vinegar, he may have sesame oil, date honey and vinegar of bad grapes.

Beis Yosef (DH u'Mah): He is permitted apple wine, because Stam wine is of grapes.