Gemara

(R. Chiya): If Reuven told Shimon 'you owe me 100', and Shimon said 'I owe only 50. Heilach (take it) and returned 50, he must swear about the other 50. This is considered admission to part of the claim. (We do not say that they argue only about the other 50, and he totally denies it!)

Support: In the Mishnah, Reuven and Shimon are holding a garment... We are witnesses that each owns half (and he must give up the other half. This is like Heilach), and still they swear!

(Rav Sheshes): One who partially admits to a claim and says 'Heilach' is exempt from swearing.

He holds that the Mishnah is only an enactment mid'Rabanan (lest people grab others' garments and claim them). R. Chiya agrees that the Mishnah is an enactment. However, Chachamim enact only what is similar to Torah law. If Heilach were exempt, they would not enact an oath unlike Torah oaths.

Question: According to Rav Sheshes, who exempts Heilach, why do we need a verse to exempt land from oaths? Every admission of land is Heilach!

Answer: We need the verse for when he damaged the land (and must pay. This is not Heilach.) Alternatively, we need the verse for an admission of Kelim (in a case that is not Heilach) and denial of land.

(Rami bar Chama): The four Shomrim swear only when they partially deny and partially admit to the claim.

Suggestion: He said 'Heilach' (and he swears)!

Rejection: No. Reuven said that he deposited three cows and all died through negligence. Shimon said that he deposited only two; one died through Ones, and one through negligence, and he owes for one. This is not Heilach.

97a (Mishnah): If Reuven borrowed Shimon's cow for one day and rented it for the next day, and Shimon claims that it died on the day it was borrowed, and and Reuven is unsure, he must pay.

98a: We can establish the Mishnah when Reuven borrowed and rented two cows. Shimon claims that both died on the day that they were borrowed. Reuven admits about one, and he is unsure about the other. Since Reuven must swear and he cannot, he must pay.

100a (Mishnah): If Reuven had two slaves (or fields), one big and one small, and Shimon says 'I bought the big one', and Reuven says 'I sold the small one', Reuven swears that he sold the small one.

Question: Why does he swear? His admission was not part of the claim, and it is Heilach, and we do not swear about slaves (or land)!

Answer (Shmuel): They argue about the clothing of a big or small slave, or the piles of grain of a big or small field.

Shevuos 43a (Mishnah): If Reuven claimed 'I entrusted you with a house full (e.g. of grain) and Shimon said 'I don't know how much it was, take what is there', he is exempt. If Reuven claimed 'it was full up to the ledge and Shimon said 'it was up to the window', he is liable.

Bava Kama 105b (Beraisa): Yehudah had Levi's ox, but denied that he stole it. He swore 'I am a Shomer Chinam', and later admitted. He does not swear, for "he denied it" excludes one who admits from the beginning.

(Rabah): The Beraisa discusses a case of Heilach. I obligate (in a case of similar claims) when the animal is in the swamp.

Rishonim

Rif and Rosh (1:5): The Sugya is like Rav Sheshes. On 100a, we asked that one should be exempt because it is Heilach.

Ba'al ha'Ma'or (1a DH Heilach): The Gemara tried to prove that Heilach is liable from the Mishnah of two holding a Talis. In the Mishnah, he does not admit! The Ra'avad says that even if one party agrees to let the other take half without an oath, he himself must swear. I say that since the Talis is here ready to be divided, it is like Heilach. R. Chiya holds that if Heilach were exempt, Chachamim would not enact an oath in this case.

Rosh: The Gemara (98a) established the Mishnah to be a case of two cows, so it would not be Heilach. In Shevuos, we obligate one who says 'it was up to the window.' This is when the Peros rotted due to his negligence and he owes for them, so it is not Heilach.

Hagahos Ashri: It is Heilach only when he returns the same coins that he lent to him or the same deposit. If he says 'I owe you only 50. Heilach', and he gives other coins, this is not Heilach and he must swear even according to Rav Sheshes. Rashi connotes like this.

Nimukei Yosef (57b DH Masnisin): Shmuel said that they argue about the clothing of a big or small slave. Since it is not specific (he must cut a small garment from a big one), it is not Heilach.

Ran (Shevuos 17b DH Garsinan): Rashi connotes that if he gives to him different coins, even if he gives to him in Beis Din, it is not Heilach. If so, Heilach applies only to a deposit. Even if one returns the same coins of a loan, he cannot say 'the coins are yours wherever they are.' We hold that Kidushin with a loan is invalid, for it is in the Reshus of the borrower, not of the lender, regarding retracting the loan and responsibility for Ones. This is unlike the Ge'onim, who say that Heilach applies to a loan or deposit, whether he returns the same coins he lent or others. Regarding a deposit, as long as he admits, even if it is not in his hand, rather, in the swamp, it is Heilach, for wherever it is, it is in the owner's Reshus. A proof for this is Bava Metzia 5b. We asked that according to Rami bar Chama, who requires Modeh b'Miktzas for Shevu'as ha'Pikadon, it is Heilach. If Heilach is only when he returns the deposit immediately, what was the question? Also, why did we need to answer that he said one died through negligence and he owes for it? We can say that it is in the swamp! Rather, any admission to an (intact) deposit is Heilach. Only a loan must be in his hand and ready to return to be considered Heilach.

Rambam (Hilchos To'en 1:3): If Reuven claimed Metaltelim from Shimon, and Shimon admitted to part and immediately gave them and said 'this is all I owe you; Heilach', he is exempt from swearing mid'Oraisa.

Rambam (3:15): If Reuven claimed 100 Zuz and a Kli, and Shimon said 'I owe you only a Kli. Here it is', he is exempt and swears Heses. If Reuven says 'this is not my Kli', and Shimon admitted that he switched his Kli for another, he must swear mid'Oraisa. If Reuven says 'this is not my Kli', and Shimon admitted that he switched his Kli for another, he must swear mid'Oraisa.

Magid Mishneh: The Rambam connotes that even regarding a deposit, if he does not say 'Heilach', even if it is intact, this is Modeh b'Miktzas. The Ramban proved otherwise from Bava Metzia 5a, for wherever it is, it is in the owner's Reshus.

Rosh (Kesuvos 2:1): When a divorcee claims that her Kesuvah was 200, and he claims that her Kesuvah was 100, he need not swear mid'Oraisa. This is like denial of a debt with a lien on land. Even after it was enacted to collect from Metaltelim, since Beis Din enacted that every woman has a Kesuvah of at least 100, he could not claim 'I paid.' Therefore, the 100 he admits to is Heilach, since he could not have evaded it, and he denied the rest.

Bedek ha'Bayis (CM 87:5): This is unlike the Poskim who say that Heilach is only when he gives the money immediately. However, the law is true, for Modeh b'Miktzas is only when he could have denied.

Poskim

Shulchan Aruch (CM 87:1): Even if Shimon admitted to part of the claim, if he said 'here is the part I admit to'; he swears only Heses. Heilach is only if the part he admits to is ready in his hand in front of Beis Din to give to him immediately, but not if he said 'it is in my house and I will give it to you.'

SMA (8): Since he gives what he admits to, regarding the rest, he totally denies.

Rebuttal (Shach 2): The Tur and Shulchan Aruch connote that Heilach applies whenever he has the money in Beis Din and is ready to return it, even before he returned it, like the Ran says.

Beis Yosef (DH v'Afilu): The Ramban and Rashba hold like the Ran. The Magid Mishneh says that the Rambam holds like Rashi. Perhaps there the Rambam said 'Heilach' to exclude when the deposit was lost or burned. However, in Halachah 1:3 the Rambam exempts 'if he immediately gave what he admits that he owes.'

Shach (3): Most Poskim exempt a deposit no matter where it is, even if in the Shomer's house. The Gemara mentioned the swamp for this is normal for a cow. All the more so it is Heilach if it is in his house. The Ra'avad challenged this from Shevuos 43a. If every deposit is Heilach, granted, we can say that Peros rotted, but how can we answer why one swears about coins?

Gra (10): Bava Kama 105b proves that an animal in the swamp is not Heilach. This refers to a loan, but a deposit is Heilach even if it is in the swamp. This is why we needed to give a different answer in Bava Metzia 5a.