The Mathematics of Logic

This undergraduate textbook covers the core material of a first course in logic. Its main result is a rigorous proof-based treatment of the Completeness Theorem for first-order logic.

No prior knowledge of formal set theory is assumed, since the set-theoretic results it needs are proved in the text. Topics run from König’s Lemma through order relations and Zorn’s Lemma to Boolean algebras and propositional logic.

Most of the material centres on first-order logic, with its completeness and compactness theorems, and the last two chapters introduce model theory. Every step is supported by explanations and exercises. Published by Cambridge University Press, 1st edition. ISBN-13: 9780521708777.