Combinatorial Set Theory: With a Gentle Introduction to Forcing

This book, now in a revised and extended third edition, provides a comprehensive and accessible introduction to modern axiomatic set theory.

After an overview of basic notions in combinatorics and first-order logic, and discussing in great detail the axioms of set theory, the author outlines in the second part the main topics of classical set theory, including Ramsey theory and the axiom of choice. As an application of the axiom of choice, a complete proof of Robinson's construction for do...