Three Short Stories around Gödel's Incompleteness Theorems

Abstract

We describe three short stories around Gödel's incompleteness theorems. Firstly, we show that the second incompleteness theorem is derivable by formalizing Yablo's paradox. Then, we prove a version of the incompleteness theorem which is not formalizable. Finally, we discuss the theorems of arithmetic in nonstandard models of arithmetic and the definability of truth in models of arithmetic within other models.