A general principle for purely model-theoretical proofs of Gödel’s second incompleteness theorem

Dirk Ullrich

DOI: http://dx.doi.org/10.12775/LLP.1998.009

Abstract


By generalizing Kreisel’s proof of the Second Incompleteness Theorem of Gödel I extract a general principle which can also be used for other purely model-theoretical proofs of that theorem.

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References


Adamowicz, Z., and P. Zbierski, Logic of Mathematics. A Modern Course of Classical Logic, John Wiley & Sons, New York 1997.

Boolos, G., The Logic of Provability, Cambridge University Press, Cambridge, 1993.

Feferman, S., “Arithmetization of metamathematics in a general setting”, Fundamenta Mathematicae XLIX (1960), p. 35–92.

Hajék, P., and P. Pudlák, Metamathematics of First-Order Arithmetic, Springer Verlag, Berlin 1993.

Kaye, R., Models of Peano Arithmetic, Clarendon Press, Oxford, 1991.

Kikuchi, M., and K. Tanaka, “On formalization of model-theoretic proofs of Gödel’s theorems”, Notre Dame Journal of Formal Logic 35 (1994), p. 403–412.

Smorynski, C., “The incompleteness theorems”, p. 821–865 in Handbook of Mathematical Logic, edited by J. Barwise, North Holland, Amsterdam, 1977.

Ullrich, D., “A purely model-theoretical proof of the Second Incompleteness Theorem of Gödel using Berry’s Paradox”, submitted to Acta Mathematica Universitatis Comenianae.








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ISSN: 1425-3305 (print version)
ISSN: 2300-9802 (electronic version)

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