Gemara

(Mishnah): If Reuven said 'one of my lambs (or bulls) is a Korban', if he has two, the larger one is a Korban. If he has three, the medium one is a Korban.

(Shmuel): The Seifa means that we are concerned even for the medium one.

(Rav Nachman): This is only if he said 'one of my bulls (is a Korban)'. If he said 'a bull of my bulls', only the biggest is a Korban, for he means 'the most important.'

Question: Rav Huna taught that if one said 'I sell to you a house of my houses', he may give to him (an) Aliyah;

Suggestion: (This refers to an attic.) It is inferior!

Answer #1: No. 'Aliyah' means (he must give) 'Me'ulah' (the best) of his houses.

Question (Beraisa): If one sold 'a house of my houses' (or, 'a slave of my slaves'), and one of them fell (died), he can say that it is the one that he sold.

According to Rav Nachman, he sold the best!

Answer: A buyer is different, for the one who bears the document has the lower hand.

This is a second answer to the first question.

Nedarim 56a (Mishnah - R. Meir): If one vowed from a house, the Aliyah is permitted;

Chachamim say, the Aliyah is part of the house;

(Rav Huna bar Chiya): If one said 'I sell to you a house among my houses', he (may) give(s) to him an Aliyah.

Inference: This is only because he said 'a house among my houses.' Had he said only 'a house', he could not give him an Aliyah!

Suggestion: This is like R. Meir.

Rejection: It can even be like Chachamim. Aliyah means Me'ulah of houses.

Bava Basra 107b (Mishnah): If Reuven told Shimon 'I sell to you half of a field', Meshamnim Beinehem. Shimon takes half a field;

(R. Yochanan): Shimon gets land worth as much as what Reuven keeps. Reuven can choose to keep the highest quality land.

Rishonim

Rambam (Hilchos Mechirah 21:19): If one said 'I sell to you a house of my houses' or 'an ox of my oxen', he may give to him the smallest. If one of them fell or died, he can give that one to him, for the one who bears the document has the lower hand.

Perush ha'Rosh (Nedarim 56a DH Leima): The Gemara suggested that R. Chiya's law is only like R. Meir. It understood that he may give an Aliyah only because he said 'a house among my houses', which connotes any house (even if it is very lowly). Chachamim would permit giving an Aliyah even if he said Stam 'house'. We reject this. Rather, 'Aliyah' means his best property. Surely, if he said Stam 'house', he may give an Aliyah. 'A house among my houses' excludes an Aliyah. It is inferior, for one must go up and down. Rather, he must give the best among the two of these (a house and an Aliyah, i.e. a house.) However, he may give the worst house he has, for the bearer of a document has the lower hand, like we conclude in Menachos.

Ran (56a DH Mai): In Menachos we conclude that Aliyah refers to an upper story; it is inferior. If so, we cannot establish Rav Huna like Rabanan, for if so, why did he say 'of my houses'? Even if he said just 'house', this includes an Aliyah. If so, perhaps the Halachah follows R. Meir. However, the Ramban (19a) says that even in the conclusion, Rav Huna is even like Chachamim. Perhaps 'house among my houses' teaches a bigger Chidush. Not only when he says 'house' Stam he can give an Aliyah, which is inferior. Rather, even when he says 'house of my houses', which connotes a superior house, regarding a buyer he can give an Aliyah. Since we can say that Rav Huna holds like Chachamim, we rule like Chachamim.

Poskim

Shulchan Aruch (CM 214:12): If one said 'I give to you a house of my houses', he may give to him the smallest. If one of them fell, he can give to him the one that fell, for the one who bears the document has the lower hand. The same applies if he said 'I sell to you an ox of my oxen.'

Rema: He cannot give to him an Aliyah. However, if he said only 'I sell to you a house', he can give to him an Aliyah, for also an Aliyah is called a house.

Beis Yosef (DH ha'Omer): The Tur wrote Stam like the Rosh, like the conclusion in Menachos (if he said Stam 'house', he may give an Aliyah. If he said 'a house among my houses', he must give a house, but he may give the worst house he has.)

SMA (48): Even though also an Aliyah is called a house, and the bearer of a document has the lower hand, since the seller said ''a house of my houses', this shows that he sells the best thing called a house. This is unlike the way the Ran, Beis Yosef and Darchei Moshe explain the Rambam, that even when he says 'a house of my houses', the seller can give an Aliyah. They derive from the Rambam's words 'he gives the lowliest.' The Rambam did not specify that it must be a house, and not an Aliyah. Even if you will say that the Rambam does not explicitly argue, the Ran explicitly argues. Perhaps the Rema did not want to elaborate, and wrote Stam, since the Rosh and Tur wrote Stam.

Gra (48): This is like the Sugya in Menachos. This is unlike the Sugya in Nedarim, which is like the Hava Amina in Menachos.

Shulchan Aruch (218:20): If one said 'I sell to you half a field', he gives an amount worth half the value from the inferior part.

Question (In Avodas ha'Gershoni 5): A case occurred in which Reuven and his wife gave to their son-in-law Shimon rights to live in half of their Dirah (dwelling) for 15 years. Reuven died after a year, and his widow and son needed to sell their half of the house, for half of it was mortgaged to Ploni, and had they not redeemed it, the buyer (Ploni) would have kept it permanently. Therefore, they sold Stam half the house absolutely to Shimon. The widow remarried, and Shimon agreed to lend to her for a dowry; the other half of the house (which she received for her Kesuvah) was collateral. Shimon would live in it, and deduct from the loan. Later, they had a quarrel, and he retracted. She wanted to use it for collateral; he protested, for half he owned totally, and the other half he has rights to live in. She said that she and her son had sold to him absolutely the half he already had rights in.

Teshuvah (Avram bar Moshe, a Talmid of the Avodas ha'Gershoni): I ruled that she is correct. Since they sold Stam half the house to Shimon, they can say that it is the half he already had rights to live in. Even if a document says that the bearer has the upper hand, this helps only when two expressions contradict each other. However, when one says 'I sell to you a house' Stam, the reason he can give the worst house is not due to Safek. Rather, the document connotes the worst. He does not have the upper hand for this. If a document says 'Dinarim', but does not say how many, if one seized more than two, he must return the excess (Beis Yosef CM 42). This is not due to Safek. Rather, a document entitles only the smallest amount connoted. We say similarly in Menachos. The bearer of a document has the lower hand, but Hekdesh has the upper hand. Therefore, if one was Makdish 'a house of my houses', the best is Hekdesh. Even so, when he was Makdish Stam 'a house', it is the smallest. Here, nothing suggests that Shimon bought the half he had no rights to. Even if you will say that he did, perhaps he was given rights in the half mortgaged to Ploni! Even if you will say that Shimon bought the half he had no rights to, and he was given rights in the half not mortgaged, when the heir redeemed it, it is as if Ploni collected it, and the heir bought it back from him (CM 107:10)! Even though if one said 'I sell to you half a field', Meshamnim Beinehem (he gives an amount worth half the value, from the inferior, if he wants) (218:20), there is different. The inferiority is due to the field itself; this will never change. Here, it is inferior only due to the document entitling Shimon to live there. Since it is temporary, there is no reason to say that it changes how we explain 'half the house.' It is unreasonable that today the words mean one thing, and afterwards they mean something else.

Rebuttal (Avodas ha'Gershoni): Shimon's purchase is not like buying a Stam house. There, he gets a small house, for it is called a house just like a big house. The same would apply here if a house in front of us was divided into two parts. Here, he said 'I sell to you half of my house.' This means half of the entire house. He cannot give to him the inferior half. If one sold 'half of a field' Shimon gets land worth half, but Reuven can keep the highest quality land. The Rashbam explains that the buyer has the lower hand. Here also, the son-in-law receives a half worth half the value of the house. However, if so, he should have rights only in three quarters of the house (half of the half he bought is what he already had rights to). One who sells, sells what he owns, i.e. half her rights in the house. However, a Stam sale is for the Guf (permanent ownership) and Peros (temporary usage). Therefore, we say that they sold the half that Shimon had no rights to. Also, the sale document said 'from now, Shimon has rights to live in it or rent it out.' Even though it also said that she keeps rights to collect her Kesuvah from the other half, these are not superfluous words to show that she sold the part he already had rights to. She needed to write that her son is not an equal partner in it. I do not say that the questioner erred in a clear matter; this is a new matter. This is my opinion.

Pischei Teshuvah (214:6): Also Teshuvas Ge'onei Basrai (58) says like the questioner (Avraham ben Moshe) that the bearer of a document receives the smallest connotation of the words.