Set Theory, Logic and their Limitations [Paperback]

Rigorous coverage of logic and set theory for students of mathematics and philosophy.This introduction to set theory and logic discusses first order logic, and provides a rigorous axiomatic presentation of Zermelo-Fraenkel set theory. It includes many methodological remarks and explanations, demonstrating how the basic concepts of mathematics can be reduced to set theory.This introduction to set theory and logic discusses first order logic, and provides a rigorous axiomatic presentation of Zermelo-Fraenkel set theory. It includes many methodological remarks and explanations, demonstrating how the basic concepts of mathematics can be reduced to set theory.In this introduction to set theory and logic, the author discusses first order logic, and gives a rigorous axiomatic presentation of Zermelo-Fraenkel set theory. He includes many methodological remarks and explanations, and demonstrates how the basic concepts of mathematics can be reduced to set theory. He explains concepts and results of recursion theory in intuitive terms, and reaches the limitative results of Skolem, Tarski, Church and Gödel (the celebrated incompleteness theorems). For students of mathematics and philosophy, this book provides an excellent introduction to logic and set theory.Mathematical induction; 1. Sets and classes; 2. Relations and functions; 3. Cardinals; 4. Ordinals; 5. The axiom of choice; 6. Finite cardinals and alephs; 7. Propositional logic; 8. First order logic; 9. Facts from recursion theory; 10. Limitative results; Appendix: Skolem's paradox. ...a concise and polished text... J.M. Plotkin, Mathematical Reviews