Elements of Set Theory
by Herbert B. Enderton · Academic Press
Undergraduate textbook developing axiomatic Zermelo-Fraenkel set theory from the ground up. Covers relations and functions, the construction of the natural and real numbers, cardinals, ordinals and the axiom of choice, leaving the reader able to work with sets rigorously.
This link may earn us a small commission at no extra cost to you. Affiliate disclosure
More resources on Set Theory
Wolfram MathWorld
MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.
ProofWiki - Set Theory
Category index on the community-maintained ProofWiki collecting formal definitions and rigorous proofs of set-theoretic results, from basic operations and relations to cardinals, ordinals, and the ZFC axioms. Useful for checking a precise statement or a complete proof step by step.
Stanford Encyclopedia of Philosophy - Set Theory
Joan Bagaria's peer-reviewed Stanford Encyclopedia of Philosophy entry surveying modern set theory: the ZFC axioms, ordinals and cardinals, the continuum hypothesis, forcing and independence results, large cardinals, and determinacy. Readers gain a map of the field's central questions and results.
Mathematics for Computer Science (MIT 6.042J)
Discrete mathematics for computer science with an emphasis on definitions and proofs: logic, induction, sets and relations, graph theory, modular arithmetic, asymptotics, counting and discrete probability. 25 lecture videos, problem sets and exams with solutions build fluency in writing proofs.
Naive Set Theory
Paul Halmos's short classic introduction to set theory, built up from the axioms of extension, specification, pairing, and choice through relations, functions, natural numbers, ordinals, and cardinals. Readers learn the set-theoretic vocabulary assumed by nearly all modern mathematics.
Set Theory: An Introduction to Independence Proofs
Graduate text that develops ZFC from the axioms through ordinals, cardinals, infinitary combinatorics and Martin's axiom, then constructible sets and forcing. Readers who finish it can follow and construct consistency proofs, including the independence of the continuum hypothesis.