Gemara

101b (R. Yochanan): If Reuven tells Shimon 'I owe you 100', he must pay;

Reish Lakish says, he need not.

Question: If Reuven said (to witnesses) 'Atem Edai (you are witnesses against me)', why would Reish Lakish exempt? If Reuven did not say 'Atem Edai', why would R. Yochanan obligate?

Answer: He did not say this. Rather, he said 'I owe you 100 in a document.' R. Yochanan says, the matter of a document is potent. It is as if he said 'Atem Edai.' Reish Lakish says, it is not potent.

Suggestion (Rava): R. Yochanan holds like R. Yishmael, and Reish Lakish holds like Ben Nanas:

(Mishnah): If a loan document says 'Ploni is an Arev (guarantor)' below the signatures (and Ploni agrees), the lender may collect from Ploni's Bnei Chorin, but not from property he sold. R. Yishmael ruled like this in practice.

Ben Nanas: Ploni is exempt, for the lender did not rely on Ploni when he lent.

Rejection: R. Yishmael can hold like Reish Lakish. R. Yishmael obligates an Arev to pay, for the Torah does. Here, there is no Torah obligation!

Sanhedrin 29a (Mishnah): We ask the witness 'how do you know that Levi owes Shimon?' If he says 'Levi himself told me', or 'Ploni told me', this is not testimony. He must say 'Levi admitted to Shimon in front of us that he owes him 200.'

This supports Rav Yehudah, who says that an admission is valid only if he said 'Atem Edai.'

Bava Basra 149a: A convert had deposited money with Rava. He was about to die, and wanted to give them to his biological son, who was elsewhere.

Rav Ika brei d'Rav Ami: He can admit that the money belongs to his son. His son will acquire through Odisa (Kinyan through (even a false) admission)!

Rishonim

Rif: We say that R. Yochanan holds like R. Yishmael, who obligates an Arev below the signatures. This shows that R. Yochanan and Reish Lakish argue about accepting a new obligation. The Halachah follows R. Yochanan, who obligates even if he did not say 'Atem Edai', all the more so if he said so, for even Reish Lakish agrees then, and all the more so, if a Kinyan (Chalipin) was done.

Rambam (Hilchos Mechirah 11:15): If Reuven obligates himself to Ploni unconditionally, even though he did not owe to him anything, he is liable. This is like a gift; it is not Asmachta. If Reuven says to witnesses 'you are witnesses against me that I owe 100 to Ploni', or he said in front of witnesses 'I owe you 100 in a document', he must pay. Even though he did not say 'Atem Edai', saying 'in a document' is like saying 'Atem Edai'. This is even if both admit and the witnesses know that he did not owe anything. He obligated himself like an Arev. The Ge'onim ruled like this.

Magid Mishneh: The Rambam explains that he comes to obligate himself. He does not say that the one who admitted later denied owing. It was clear to the Gemara that 'Atem Edai' helps to obligate oneself, just like it helps for admissions. The Ramban and Rashba disagree. If there was no prior debt, we would not ask why Reish Lakish exempts, rather, why R. Yochanan obligates! Later, we answer that he obligates himself through a document.

Ran (61b DH Gemara and Sof DH Hacha): One cannot accept a new obligation without receiving money, or a Kinyan, or a document. Also an Arev obligates himself only through a Kinyan, or through the Hana'ah that money was lent due to him. The Gemara needed to say that a Kinyan was made to explain how a Shomer can accept more obligations than Torah law (Bava Metzi'a 58a and 94a). The Rif and Rambam hold that one can accept a new obligation through mere speech. They must explain that we could also have said that the Shomer obligated himself by saying 'Atem Edai.' Surely we could also have said that he obligated himself through a document! The Gemara discussed Kinyan, for this is the normal case.

Gra (CM 40:2 DH u'Mah she'Chosav): The Rambam holds that we needed to explain that an Arev obligates himself through Hana'ah, for it is Asmachta. If a Shomer accepts extra obligations without a Kinyan, this is Asmachta.

Rosh (12:2): Rashi explains that we discuss one who admitted 'I owe you', but he did not sign. R. Tam explains that he did not admit; he wrote in his handwriting 'I owe you' and obligated himself through the document. The Rif agrees.

Question (Hagahos Ashri): In Sanhedrin, it seems that he need not say 'Atem Edai', as long as he knows that the witnesses are there. The Mishnah does not mention 'Atem Edai', yet the Gemara says that it supports Rav Yehudah, who requires this! Our Gemara connotes that he must say 'Atem Edai' even if he knows that there are witnesses there.

Poskim

Shulchan Aruch (CM 40:1): If Reuven obligates himself to Ploni unconditionally, even though he did not owe to him anything, he is liable. If Reuven says to witnesses 'you are witnesses against me that I owe 100 to Ploni', or he said in front of witnesses 'I owe you 100 in a document', he must pay.

Question (SMA 1): Why does the Shulchan Aruch say this without dissent? Many require writing or saying 'in a document' to create a new obligation!

Shach (2): Many say that even saying 'in a document' does not help. One must write a document! Rashi requires a Kinyan in addition to the document!

Nesivos ha'Mishpat (Urim 1): All agree that a Stam admission works. This is Odisa (Bava Basra 149a). They argue about when he explicitly said that he was not liable beforehand.

Shulchan Aruch (ibid.): Even though he did not say 'Atem Edai', saying 'in a document' is like saying 'Atem Edai.'

Beis Yosef (DH veha'Rif): The Rif said 'all the more so if he said Atem Edai.' The Ran and Magid Mishneh infer that the Rif holds like the Rambam, that he said 'I owe you through a document.' If he wrote a document, this is not a Kal va'Chomer! The Ramban says that the Rif holds that in the conclusion, he accepted a new obligation (and wrote a document); the Kal va'Chomer refers back to an admission. The Rosh says all the more so, if they made a Kinyan. Perhaps this was his text of the Rif.

Beis Yosef (DH mi'Kol): R. Tam obligates him only if he wrote a document. Rashi, the Ramban and Rashba hold that also Atem Edai helps. The Rambam, Ramah and Rif (according to the Ran and Magid Mishneh) hold that saying I owe you in a document also helps. We follow the Rambam, because he says that Ge'onim ruled like this, and some say that the Rif agrees.

Drishah (1): The Tur brings the three opinions. He says 'and R. Tam explained ... and the Ramah explained...', not but R. Tam says... He concludes 'and so says the Rambam.' This suggests that the Tur holds that they argue only about how to explain the Gemara, but not about the Halachah. Also Tosfos did not say that R. Tam argues with Rashi l'Halachah. However, Hagahos Ashri holds that they argue, for he asks, according to Rashi, how he obligated himself. If he gave a Kesav Yado, without signing it, not in front of witnesses, Rashi and R. Tam disqualify it. It seems that the Rambam would be Machshir, but perhaps he merely cited the Gemara.

Shulchan Aruch (ibid.): This is even if both admit and the witnesses know that he did not owe anything.

Source (Gra 4): We learn from Odisa (Bava Basra 149a, Tosfos DH Shechiv).

Shulchan Aruch (ibid.): He obligated himself like an Arev.

SMA (2) and Prishah (4): An Arev becomes obligated even without a Kinyan, even after the loan was given, if the Arvus was written before the witnesses signed. It works due to the Hana'ah that he is written in the document.

Rejection (Shach 7): The Rambam (Hilchos Malveh 26:1), Tur and Shulchan Aruch (129:4) all require a Kinyan! Rather, they teach that one accepts a new obligation, like an Arev.