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Theorems of Tarski's Undefinability and Godel's Second Incompleteness-Computationally (1509.00164v3)
Published 1 Sep 2015 in math.LO and cs.LO
Abstract: We present a version of G\"odel'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 G\"odel's First Incompleteness Theorem relativized to definable oracles; a unification of these two theorems is given.