Del i serien Cambridge Mathematical Textbooks

Set Theory

A First Course

Häftad, Engelska, 2026

AvDaniel W. Cunningham

789 kr

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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.

Produktinformation

Utgivningsdatum2026-12-31
FormatHäftad
SpråkEngelska
SerieCambridge Mathematical Textbooks
Antal sidor326
Upplaga2
FörlagCambridge University Press
ISBN9781009583404

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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).

Praise for the first edition: '… Cunningham neglects no opportunity to make the subject as accessible as possible. The mathematical development is rigorous, as it should be, but not excessively so. Although he starts from zero, that is not to say the book is easy, but any difficulty that arises is in the nature of the subject, and is no fault of the author's. Throughout the book, he offers many appropriate examples (or non-examples), and provides numerous and diverse exercises, which often prove results that are later used in the body of the text, drawing the reader into the subject.' Frederic Green, ACM SIGACT News