Contents: Introduction; First-order Validity; The Soundness Theorem for First-order Logic; The Completeness Theorem for Truth-functional Logic; The Completeness Theorem for First-order Logic; Preliminaries Before We Take On Gödel-incompleteness; Sets of Numbers; Diagonalization; Arithmetization of Syntax and the First Incompleteness Theorem; Definability in a Theory; The Upper Diagonal Lemma and Some Consequences; The Undecidability of First-order Logic; Gödel’s Second Incompleteness Theorem; Second-order Logic; Propositional Modal Logic; Quantified Modal Logic |