Gödel Without Tears by Peter Smith

A clear, friendly introduction to Gödel’s incompleteness theorems that gently builds the needed background in first-order logic and formal arithmetic, explains core ideas like arithmetization of syntax, Gödel numbering, representability, and diagonalization, and then presents careful proofs of the first and second theorems, with brief excursions to related results such as Rosser’s strengthening and Tarski’s undefinability of truth, all aimed at readers seeking an accessible but rigorous path through the subject.

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