Set Theory, Logic and their Limitations

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.

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.