Formal Background for the Incompleteness and Undefinability Theorems

Abstract

A teaching document I've used in my courses on truth and on incompleteness. Aimed at students who have a good grasp of basic logic, and decent math skills, it attempts to give them the background they need to understand a proper statement of the classic results due to Gödel and Tarski, and sketches their proofs. Topics covered include the notions of language and theory, the basics of formal syntax and arithmetization, formal arithmetic (Q and PA), representability, diagonalization, and the incompleteness and undefinability theorems.

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Richard Kimberly Heck
Brown University

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2022-08-14

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