**Translations of Mathematical Monographs**

1988;
228 pp;
Softcover

MSC: Primary 03;

Print ISBN: 978-0-8218-4520-2

Product Code: MMONO/67

List Price: $88.00

AMS Member Price: $70.40

MAA Member Price: $79.20

**Electronic ISBN: 978-1-4704-4481-5
Product Code: MMONO/67.E**

List Price: $88.00

AMS Member Price: $70.40

MAA Member Price: $79.20

# Mathematical Intuitionism: Introduction to Proof Theory

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*A. G. Dragalin*

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

# Table of Contents

## Mathematical Intuitionism: Introduction to Proof Theory

- Cover Cover11
- Title page iii4
- Contents v6
- Preface vii8
- Logic 112
- Arithmetic 2334
- Algebraic models 5970
- Analysis 125136
- Eliminability of cuts in the intuitionistic simple theory of types in the form of a sequent calculus with extensionality 153164
- Appendix A: An algebraic approach to models of realizability type 173184
- Appendix B: A strong form of the normalization theorem 185196
- Bibliography 201212
- Index of names 217228
- Subject index 219230
- Names of formal theories 225236
- Names of axioms and rules of inference 226237
- Notation for formulas and terms 227238
- Realizabilities 228239
- Back Cover Back Cover1241