Set Theory

Daniel W. Cunningham is a Professor of Mathematics at State University of New York, Buffalo, specializing in set theory and mathematical logic. He is a member of the Association for Symbolic Logic, the American Mathematical Society, and the Mathematical Association of America. Cunningham's previous work includes A Logical Introduction to Proof, which was published in 2013.

• 1. Introduction; 2. Basic set building axioms and operations; 3. Relations and functions; 4. The natural numbers; 5. On the size of sets; 6. Transfinite recursion; 7. The axiom of choice (revisited); 8. Ordinals; 9. Cardinals.

'… 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