In the area of mathematical logic, a great deal of attention is now being devoted to the study of nonclassical logics. Nonclassical logics are used in the theory of computations, in information theory, and for the description of systems of heuristic programming. Intuitionistic logic is a particularly important nonclassical logic. The aim of this book is to present the most important methods of proof theory in intuitionistic logic and to acquaint the reader with the principal axiomatic theories based on intuitionistic logic. The exposition, accessible to a wide audience, requires only an introductory course in classical mathematical logic.

Table of Contents

• Logic
• Arithmetic
• Algebraic models
• Analysis
• Eliminability of cuts in the intuitionistic simple theory of types in the form of a sequent calculus with extensionality
• Appendix A: An algebraic approach to models of realizability type
• Appendix B: A strong form of the normalization theorem