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We present a version of G\"odel's Second Incompleteness Theorem forrecursively enumerable consistent extensions of a fixed axiomatizable theory,by incorporating some bi-theoretic version of the derivability conditions. Wealso argue that Tarski's theorem on the Undefinability of Truth is G\"odel'sFirst Incompleteness Theorem relativized to definable oracles; a unification ofthese two theorems is given.

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