Axiomatic Set Theory

An Introduction
Erscheinungsjahr 2026
ISBN: 978-3-032-10039-9
Verlag: Springer-Verlag GmbH

Buch, Englisch, 307 Seiten, Format (B × H): 168 mm x 240 mm

Reihe: Synthesis Lectures on Mathematics & Statistics

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.

Zielgruppe

Upper undergraduate

Autoren/Hrsg.

Tourlakis, George

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik
• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker
• Mathematik | Informatik Mathematik Mathematik Allgemein Mengenlehre
• Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik
• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik

Inhaltsverzeichnis

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

Über Autor(innen)

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.