Undefinability of truth and nonstandard models
type: Item
instance of: scholarly article
title: Undefinability of truth and nonstandard models
zbMATH Open document ID: 1063.03021
author: Roman Kossak
published in: Annals of Pure and Applied Logic
publication date: 2004-08-06T00:00:00Z
review text: Let \(\mathbb N=(\omega,+,\times,<,0,1)\) be the standard model of Peano Arithmetic (PA). Tarski's theorem on the undefinability of truth claims that the set TA \(=\{\phi: \mathbb N \models \phi\}\) is undefinable in \(\mathbb N\). \textit{A. Robinson} gave a model-theoretic proof of Tarski's theorem [Nagoya Math. J. 22, 83--117 (1963; Zbl 0166.26101)]. In the paper the author discusses Robinson's proof of Tarski's theorem and gives two other ``diagonal-free'' proofs. In Notre Dame J. Formal Logic 36, 519--530 (1995; Zbl 0848.03016), the author posed a problem about a possible converse to Tarski's theorem. In this paper he presents some arguments in favor of a negative answer to this question. Finally, the author poses another open problem: Is there an easy proof of Ehrenfeucht's lemma from Tarski's theorem?
reviewed by: M. Ya. Komarnitskiy
Mathematics Subject Classification ID: 03C62
Mathematics Subject Classification ID: 03H15
Mathematics Subject Classification ID: 03F30
Mathematics Subject Classification ID: 11U10
Mathematics Subject Classification ID: 12L15
zbMATH DE Number: 2083175
zbMATH Keywords: models of arithmetic
zbMATH Keywords: undefinability of truth
zbMATH Keywords: recursive saturation
zbMATH Keywords: satisfaction classes
MaRDI profile type: Publication
full work available at URL: j.apal.2003.10.011
OpenAlex ID: W2007908701
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DOI: 10.1016/J.APAL.2003.10.011
description: scientific article; zbMATH DE number 2083175