Synthesis Lectures on Mathematics & Statistics- 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. The axioms of (ZFC) set theory are introduced with natural axiomatizations and informal justifications, which is relatively distinctive. 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.