Set Theory

A First Course
2. Auflage 2026
ISBN: 978-1-009-58340-4
Verlag: Cambridge University Press

Buch, Englisch, 326 Seiten

Reihe: Cambridge Mathematical Textbooks

This undergraduate textbook carefully introduces the fundamentals of axiomatic set theory; a rich and beautiful subject whose fundamental concepts permeate virtually every branch of mathematics. One can thus say that set theory is a foundation for mathematics. The proofs are rigorous, clear, and complete, while remaining accessible to undergraduates who are new to upper-level mathematics. Topics covered include relations, functions, the natural numbers, order, cardinality, transfinite recursion, the axiom of choice, ordinal numbers, and cardinal numbers. Exercises are given at the end of each section in a chapter. The second edition includes a new chapter on set-theoretic constructions of the integers, the rational numbers, and the real numbers; a new chapter on models of set theory. There are also new sections on the hyperreals and applications of stationary sets, club sets, and Fodor's Theorem, as well as additional explanation, examples, and figures. A solutions manual is available for instructors.

Autoren/Hrsg.

Cunningham, Daniel W.

Inhaltsverzeichnis

Preface; The Greek alphabet; 1. Introduction; 2. Basic set-building axioms and operations; 3. Relations and functions; 4. The natural numbers; 5. Constructing more number systems; 6. On the size of sets; 7. Transfinite recursion; 8. The axiom of choice (revisited); 9. Ordinals; 10. Cardinals; 11. Models of set theory; Bibliography; Index of special symbols; Index.

Über Autor(innen)

Cunningham, Daniel W.
Daniel W. Cunningham is Professor Emeritus of Mathematics at SUNY Buffalo State, a campus of the State University of New York. He received a Ph.D. in Mathematics from UCLA, specializing in set theory and mathematical logic. He currently teaches at California State University at Fresno. He is a member of the Association for Symbolic Logic, the American Mathematical Association, and the Mathematical Association of America. His research focus is on set theory, and he has published research papers in the subject. He is also the sole author of the following textbooks: Mathematical Logic: An Introduction (2023), Real Analysis: With Proof Strategies (2021), and A Logical Introduction to Proof (2013).