Theorems of Tarski's Undefinability and Godel's Second Incompleteness-Computationally
arXiv:1509.00164
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.
12 pages