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.

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

Autorentext

George Tourlakis, Ph.D., is a University Professor in the Department of Electrical Engineering and Computer Science at York University, Toronto, Canada. He obtained his B.Sc. in mechanical and electrical engineering from the National Technical University of Athens and his M.Sc. and Ph.D. in computer science from the University of Toronto. Dr. Tourlakis has authored nine books in computability, logic, and axiomatic set theory and has also authored several journal articles in computability and modal logic. His research interests include calculational logic, modal logic, proof theory, computability with partial oracles, and complexity theory.

Inhalt

The Foundations of Logic.- (Axiomatic) Set Theory.- The Axiom of Choice.- The Natural Numbers: Transitive Closure.- Order.- Cardinality.