Logic and Set Theory

Contents: 1. Logic--part I. 2. Logic--part II. 3. Group problems. 4. Set theory--part I. 5. Set theory--part II. 6. Set theory--part III. 7. Axiomatic Set Theory. 8. Naive Set Theory. 9. Rough set. 10. Higher Order Set Theory. 11. Topology. 12. Fuzzy sets and systems.

"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 Godel (the celebrated incompleteness theorems). For students of mathematics and philosophy, this book provides an excellent introduction to logic and set theory. 

Lucidly and gradually explains sets and relations, the natural number sequence and its generalization, extension of natural numbers to real numbers, logic, informal axiomatic mathematics, Boolean Algebras, Informal Axiomatic Set Theory, Several Algebraic Theories, and First-Order Theories. Its clarity makes this book excellent for self-study." (jacket)