Tarski’s Undefinability Theorem and the Diagonal Lemma

DOI10.1093/JIGPAL/JZAB016zbMATH Open1506.03126arXiv2009.00315OpenAlexW3163394101WikidataQ124814266 ScholiaQ124814266MaRDI QIDQ5092563

Author name not available (Why is that?)

Publication date: 22 July 2022

Published in: Logic Journal of the IGPL (Search for Journal in Brave)

Abstract: We prove the equivalence of the semantic version of Tarski's theorem on the undefinability of truth with a semantic version of the Diagonal Lemma, and also show the equivalence of syntactic Tarski's Undefinability Theorem with a weak syntactic diagonal lemma. We outline two seemingly diagonal-free proofs for these theorems from the literature, and show that syntactic Tarski's theorem can deliver G"odel-Rosser's Incompleteness Theorem.

Full work available at URL: https://arxiv.org/abs/2009.00315

zbMATH Keywords

self-referenceGödel's incompleteness theoremRosser's theoremdiagonal lemmaTarski's undefinability theoremdiagonal-free proofs

Mathematics Subject Classification ID

First-order arithmetic and fragments (03F30) Gödel numberings and issues of incompleteness (03F40)

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Title not available (Why is that?) ⋮ Diagonalisation and Church's Thesis: Kleene's Homework

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