ABSTRACT

This volume presents a novel approach to set theory that is entirely operational. This approach avoids the existential axioms associated with traditional Zermelo-Fraenkel set theory, and provides both a foundation for set theory and a practical approach to learning the subject. It is written at the professional/graduate student level, and will be of interest to mathematical logicians, philosophers of mathematics and students of theoretical computer science.

chapter Chapter 1|22 pages

Operations and Predicates

chapter Chapter 2|27 pages

Replacement

chapter Chapter 3|25 pages

Set Induction

chapter Chapter 4|21 pages

Applications

chapter Chapter 5|26 pages

Set Recursion

chapter Chapter 6|32 pages

Ordinals

chapter Chapter 7|20 pages

Omega

chapter Chapter 8|21 pages

Power-Set and Cardinals

chapter Chapter 9|19 pages

Formalization: Classical Logic

chapter Chapter 10|19 pages

Formalization: Intuitionistic Logic