Tarski’s Undefinability Theorem and the Diagonal Lemma

Logic Journal of the IGPL 30 (3):489-498 (2022)
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Abstract

We prove the equivalence of the semantic version of Tarski’s theorem on the undefinability of truth with the semantic version of the diagonal lemma and also show the equivalence of a syntactic version of 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 the syntactic version of Tarski’s theorem can deliver Gödel–Rosser’s incompleteness theorem.

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Saeed Salehi
University of Tabriz

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References found in this work

An Introduction to Gödel's Theorems.Peter Smith - 2009 - Bulletin of Symbolic Logic 15 (2):218-222.
A Mathematical Introduction to Logic.Herbert Enderton - 2001 - Bulletin of Symbolic Logic 9 (3):406-407.
Kleene's amazing second recursion theorem.Yiannis N. Moschovakis - 2010 - Bulletin of Symbolic Logic 16 (2):189 - 239.
The incompleteness theorems after 70 years.Henryk Kotlarski - 2004 - Annals of Pure and Applied Logic 126 (1-3):125-138.

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