Other Proofs of Old Results

Mathematical Logic Quarterly 44 (4):474-480 (1998)
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Abstract

We transform the proof of the second incompleteness theorem given in [3] to a proof-theoretic version, avoiding the use of the arithmetized completeness theorem. We give also new proofs of old results: The Arithmetical Hierarchy Theorem and Tarski's Theorem on undefinability of truth; the proofs in which the construction of a sentence by means of diagonalization lemma is not needed

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Citations of this work

Current Research on Gödel’s Incompleteness Theorems.Yong Cheng - 2021 - Bulletin of Symbolic Logic 27 (2):113-167.
The incompleteness theorems after 70 years.Henryk Kotlarski - 2004 - Annals of Pure and Applied Logic 126 (1-3):125-138.
Undefinability of truth and nonstandard models.Roman Kossak - 2004 - Annals of Pure and Applied Logic 126 (1-3):115-123.
The Scope of Gödel’s First Incompleteness Theorem.Bernd Buldt - 2014 - Logica Universalis 8 (3-4):499-552.

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References found in this work

The incompleteness theorems.Craig Smorynski - 1977 - In Jon Barwise (ed.), Handbook of mathematical logic. New York: North-Holland. pp. 821 -- 865.
Models of Peano Arithmetic.Richard Kaye - 1991 - Clarendon Press.

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