Theorems of Tarski's Undefinability and Godel's Second Incompleteness-Computationally

2015/09/01 by Saeed Salehi, Salehi, Saeed
Computer Science · Mathematics · #03A05 #03B25 #03D35 #03F40 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Computer and information sciences #FOS: Mathematics #Logic (math.LO) #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge

paper · pdf · doi:10.48550/arxiv.1509.00164

openalex publication_date 2015/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a version of Gödel's Second Incompleteness Theorem for recursively enumerable consistent extensions of a fixed axiomatizable theory, by incorporating some bi-theoretic version of the derivability conditions. We also argue that Tarski's theorem on the Undefinability of Truth is Gödel's First Incompleteness Theorem relativized to definable oracles; a unification of these two theorems is given.

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