Sets, Logic, Computation: An Open Introduction to Metalogic (Open Logic Project Textbooks)

A textbook on the semantics, proof theory, and metatheory of first-order logic. Covers naive set theory, first-order logic, sequent calculus and natural deduction, the completeness, compactness, and Löwenheim-Skolem theorems, Turing machines, and the undecidability of the halting problem and of first-order logic. It is based on the Open Logic project, and available for free download at slc.openlogicproject.org.