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Set Theory A First Course

Coming soon in December 2026

Authors

Daniel W. Cunningham
, California State University, Fresno

Description

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…

New in this edition

  • New chapter on set-theoretic constructions of the integers, the rational numbers, and the real numbers

  • New chapter on relativization and models of set theory

  • New sections covering the hyperreals and applications of stationary sets, club sets, and Fodor’s Theorem

  • Additional explanation in the more involved proofs, as well as more examples and figures

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Key features

  • Provides detailed and rigorous proofs that are accessible to readers new to upper-level mathematics
  • Reviews the basics of logic and set theory that will be assumed in the remaining parts of the book
  • The second edition features a new chapter on set-theoretic constructions of the integers, the rational numbers, and the real numbers, and a new section on constructing the hyperreals

About the book

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