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ON THE DIAGONAL LEMMA OF GÖDEL AND CARNAP

Part of: Proof theory and constructive mathematics

Published online by Cambridge University Press:  11 June 2020

SAEED SALEHI
SAEED SALEHI*
Affiliation:
RESEARCH INSTITUTE FOR FUNDAMENTAL SCIENCES UNIVERSITY OF TABRIZ, 29 BAHMAN BOULEVARD P.O. BOX 51666-16471, TABRIZ, IRAN Email: [email protected] URL: www.SaeedSalehi.ir
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Abstract

A cornerstone of modern mathematical logic is the diagonal lemma of Gödel and Carnap. It is used in, for example, the classical proofs of the theorems of Gödel, Rosser, and Tarski. From its first explication in 1934, just essentially one proof has appeared for the diagonal lemma in the literature; a proof that is so tricky and hard to relate that many authors have tried to avoid the lemma altogether. As a result, some so-called diagonal-free proofs have been given for the above-mentioned fundamental theorems of logic. In this paper, we provide new proofs for the semantic formulation of the diagonal lemma, and for a weak version of the syntactic formulation of it.

Keywords

diagonal lemmaself-referenceGödel’s incompleteness theoremTarski’s undefinability theoremBerry’s paradoxCarnap

MSC classification

Primary: 03F40: Gödel numberings and issues of incompleteness
Secondary: 03F30: First-order arithmetic and fragments
Type
Articles
Information
Bulletin of Symbolic Logic , Volume 26 , Issue 1 , March 2020 , pp. 80 - 88
Copyright
© The Association for Symbolic Logic 2020

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