Set Theory

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).

• 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.

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