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Gregor Lafitte's short paper: "G\"odel incompleteness revisited" is is a freely downloadable nice and concise overview of different kinds of proofs with a long list of references:

hal.archives-ouvertes.fr/docs/00/27/45/64/PDF/74-89.pdf

Supplement of 11th October 2011:

In a recent paper The Surprise Examination Paradox and the Second Incompleteness Theorem', Notices of the AMS Volume 57, Number 11 (it can be downloaded from http://www.ams.org/notices/201011/rtx101101454p.pdf), the authors give a new proof for Godel’s second incompleteness theorem, based on Kolmogorov complexity, Chaitin’s incompleteness theorem, and an argument that resembles the surprise examination paradox.

Gregor Lafitte's short paper: "G\"odel incompleteness revisited" is is a freely downloadable nice and concise overview of different kinds of proofs with a long list of references:

hal.archives-ouvertes.fr/docs/00/27/45/64/PDF/74-89.pdf

Supplement of 11th October 2011:

In a recent paper The Surprise Examination Paradox and the Second Incompleteness Theorem', Notices of the AMS Volume 57, Number 11 (it can be downloaded from http://www.ams.org/notices/201011/rtx101101454p.pdf), the authors give a new proof for Godel’s second incompleteness theorem, based on Kolmogorov complexity, Chaitin’s incompleteness theorem, and an argument that resembles the surprise examination paradox.

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Gregor Lafitte's short paper: "G\"odel incompleteness revisited" is is a free freely downloadable nice and concise overview of different kinds of proofs with a long list of references:

hal.archives-ouvertes.fr/docs/00/27/45/64/PDF/74-89.pdf

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