Axiomatic Set Theory

This book discusses set theory as the foundation and language of all mathematics and how axiomatic set theory benefits from advances in logic.  Chapters are written to be accessible and formative for majors in mathematics, computer science, and philosophy.  The author presents the important tools and topics including relations and functions, the concept of order, induction and inductive definitions, Cantor’s diagonalisation as well as ordinals and cardinals.  The axioms of (ZFC) set theory are introduced with natural axiomatizations and informal justifications, which is relatively distinctive. Interesting topics such as computing the support of sets by a recursively defined function and the von Neumann Hierarchy are included. In addition, this book:
- Uniquely approaches axiomatic set theory with atoms (urelements)
- Presents tools including diagonalisation, cardinality, induction, and inductive definitions
- Features a rigorous chapter on formal logic and gradually introduces and uses the axioms of (ZFC) set theory