Gemara

29a (Mishnah): If he says 'Reuven himself told me' (this is invalid). He must say 'Reuven admitted to Shimon in front of us that he owes him 200.'

This supports Rav Yehudah.

(Rav Yehudah): An admission is valid only if he said 'you are witnesses against me.'

R. Chiya bar Aba taught similarly.

(R. Chiya bar Aba): If Reuven admitted to Shimon that he owes him 100, and tomorrow he says 'I was only joking', he is exempt.

Support (Beraisa): If Reuven admitted to Shimon that he owes him 100, and tomorrow he says 'I was only joking', he is exempt. Further, if Shimon hid witnesses in back of the fence, and Reuven admitted to Shimon, and Shimon asked 'would you like to admit in front of Ploni and Almoni', and Reuven said 'no, I fear lest they take me to Beis Din', and tomorrow Reuven says 'I was only joking', he is exempt. We do not suggest claims to a Mesis (enticer to idolatry).

The Beraisa is abbreviated. It means as follows. If Reuven did not claim that he was joking, we do not claim for him. In capital cases, except for a Mesis, even if he does not claim for himself, we suggest claims to exempt him;

(Abaye): Reuven is exempt only if he claims that he was joking, but if he denies that he admitted, he is established to be a liar, and he is Chayav.

(Rava): One does not remember meaningless things.

Levi hid witnesses in back of curtains around the bed and claimed 100 from Yehudah. Yehudah admitted. Levi asked 'may the waking and sleeping be witnesses?', and Yehudah said 'no'.

(Rav Kahana): He did not want them to be witnesses (he is exempt)!

(Ravina): Rav Yehudah taught that he must say 'you are witnesses' for the admission to be valid. This episode teaches that it suffices for the lender to say it and the borrower to be silent. Had he not said 'no,' he would have been Chayav!

43b (Ravina): "Sen (Lo) Sodah" - Yehoshua made Achan think that he merely desires a confession, but he will not be killed.

Rishonim

Rif: Even if he denies that he admitted, he is exempt. One does not remember meaningless things.

Nimukei Yosef: If he said 'you are my witnesses', he is not believed to say that he was joking or he admitted falsely. One who does so does not tell people to be witnesses about this. Even if he made a proper admission to the lender, e.g. 'I do not want to admit in front of Ploni and Almoni, for I fear lest they take me to Beis Din', if he was unaware of the witnesses, he can say that he was joking. If the lender did not claim from him, he cannot say that he was joking, so he is liable.

Nimukei Yosef (DH d'Ka): Rashi and R. Chananel explain that if Reuven does not claim that he was joking, rather, he says 'I will not pay you until you bring witnesses who saw you lend to me', we do not claim for him. Rather, we say 'since you admitted, go pay.' The Rif and Rambam say that even if he says 'I never admitted', he is exempt. Beis Din does not claim for him if he admits that he admitted, but denies owing. He himself must give the reason why he admitted falsely.

Beis Yosef (32 DH Reuven): I say that both agree that the borrower must explain himself. If he denies that he admitted, the Halachah follows Rava, who exempts.

Rambam (Hilchos To'en 6:6): If Shimon said to Reuven 'you owe to me 100', and Reuven said in front of witnesses 'yes', and tomorrow when Shimon demands payment, Reuven says 'I was only joking. I owe you nothing', or even if he says nothing happened (I never admitted), he is exempt. He must swear that he does not owe to him. This is because he did not say 'you are witnesses against me.' People do not remember what is not testimony. Therefore, if he said nothing happened, he is not HucHazamahak Kafran (established to be a liar).

Rosh (3:25): Rav Sadya Gaon says that he must swear that he did not sincerely admit, rather, he was jesting. Presumably, since Shevu'as Heses was enacted for (full) denial, one must swear about any claim to exempt himself.

Poskim

Shulchan Aruch (CM 81:1): If Shimon said to Reuven 'you owe to me 100', and Reuven said in front of witnesses 'yes', and tomorrow when Shimon demands payment, Reuven says 'I was only joking', he is believed. He must swear that he was joking.

SMA (2 and Shach 2): He must include in the oath that he does not owe anything to him, like the Rambam says. The Tur and Shulchan Aruch did not mention this, for it is obvious.

Shach (1): Alternatively, he can say 'I mistakenly admitted.' This is a better claim than 'I was joking.' The Gemara derived that he is believed to say 'I was joking' because it says 'his words have no effect.'

Shulchan Aruch (ibid): Even if he did not claim 'I was joking', rather, nothing happened (I never admitted), he is exempt, for people do not remember empty (i.e. inconsequential) matters.

SMA (3): He is exempt when he says that he never admitted. If he admits that he admitted, but says that he is exempt, without giving a reason why he admitted, he must pay.

Shach (3): Even though we do not claim 'I was joking' for someone, that is when he admits that he admitted. If he denies admitting, we suggest that he was joking, and this is why he does not remember. Ba'al ha'Itur explicitly says so.

Rema: We claim 'I was joking' only for an individual who admits, but not for a Tzibur that admits, for a Tzibur does not normally jest.

Source: Rivash (476, cited in Beis Yosef 32 DH v'Ha).

Shulchan Aruch (5): The claim 'I was joking' helps only if the lender claimed from him. If he admitted on his own, he cannot say 'I was joking.'

Beis Yosef (32 DH u'Mah she'Chosav Rabeinu): Rashi explains that one can say 'since you claimed from me what I do not owe you, I answered you in jest.'

Beis Yosef (32 DH v'Chosav): The Mordechai says that if the defendant says that he was joking, if the claimant does not demand that he swear about this, we claim for him. The Rambam says (Stam) that the defendant swears. The Mordechai and R. Yerucham say so about a defendant, but not a claimant. I.e. if people told David that Moshe owes to him 200, and David said that he owes only 100, or if David said by himself that Moshe owes to him 100, and later David claims 200 from him, Moshe needs to pay only 100. He swears Modeh b'Miktzas that he owes only 100. Sefer ha'Terumos says that if one admits in front of witnesses 'I received this amount from what you owe me', he need not say 'you are witnesses against me,' even if he has a document. The same applies to admission in which one exempts another.

B'Tzel ha'Chachmah (2:58:1,5): If one or Beis Din said 'admit, and I will exempt you,' and he admitted, can he retract and say that he admitted only on condition to be exempt? Pischei Sha'arim (Sanhedrin 43b DH Klum) wanted to prove that he cannot, for if so Achan would have retracted after his admission. Do not say that just like it was a Hora'as Sha'ah (a ruling unlike the Halachah for a special case) to stone him, it was a Hora'as Sha'ah that he cannot retract. Surely, if normally his admission is invalid, also here. Pischei Sha'arim holds that he was killed only due to his admission, therefore, surely he would have retracted if possible. I say that there is no proof. Ravina said that Yehoshua bribed Achan with words. Rashi explains that Achan thought that they merely want a confession, but he will not be killed. I.e. Yehoshua did not explicitly say so. His words could mean either way. Achan understood that he will not be killed. Surely we must say so. Heaven forbid to say that Yehoshua explicitly said that he will be exempt, but did not fulfill his promise and killed him! Achan tricked himself. If so, there is no proof to one who was explicitly told that he will be exempt. Also, Achan said where he buried the things he took, and they were found where he said. This is Raglayim l'Davar (grounds to believe) that he really took them.