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2000 Nonstandard Models and Kripke's Proof of the Gödel Theorem
Hilary Putnam
Notre Dame J. Formal Logic 41(1): 53-58 (2000). DOI: 10.1305/ndjfl/1027953483

Abstract

This lecture, given at Beijing University in 1984, presents a remarkable (previously unpublished) proof of the Gödel Incompleteness Theorem due to Kripke. Today we know purely algebraic techniques that can be used to give direct proofs of the existence of nonstandard models in a style with which ordinary mathematicians feel perfectly comfortable--techniques that do not even require knowledge of the Completeness Theorem or even require that logic itself be axiomatized. Kripke used these techniques to establish incompleteness by means that could, in principle, have been understood by nineteenth-century mathematicians. The proof exhibits a statement of number theory--one which is not at all "self referring"--and constructs two models, in one of which it is true and in the other of which it is false, thereby establishing "undecidability" (independence).

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Hilary Putnam. "Nonstandard Models and Kripke's Proof of the Gödel Theorem." Notre Dame J. Formal Logic 41 (1) 53 - 58, 2000. https://doi.org/10.1305/ndjfl/1027953483

Information

Published: 2000
First available in Project Euclid: 29 July 2002

zbMATH: 1005.03054
MathSciNet: MR1915131
Digital Object Identifier: 10.1305/ndjfl/1027953483

Subjects:
Primary: 03
Secondary: 03C62, 03H15

Rights: Copyright © 2000 University of Notre Dame

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