The Foundations of Intuitionistic Mathematics
Especially in Relation to Recursive Functions
Published on 14. May 2014
215 pages
978-0-08-095759-3 (ISBN)
Description
The Foundations of Intuitionistic Mathematics
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Lev D. Beklemishev
Provability, Computability and Reflection: Volume 39
Book
04/2000
Elsevier
€210.46
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Content
- Front Cover
- The Foundations of Intuitionistic Mathematics: Especially in Relation to Recursive Functions
- Copyright Page
- Preface
- Table of Contents
- CHAPTER I. A FORMAL SYSTEM OF INTUITIONISTIC ANALYSIS
- 1. Introduction (to the monograph)
- 2. Status of the formal system
- 3. Formation rules
- 4. Postulates for predicate calculus, for number theory, and concerning functions (Postulate Groups A-C)
- 5. Postulates for certain primitive recursive functions, and consequences (Postulate Group D)
- 6. Postulate on spreads (the bar theorem)
- 7. Postulate on correlation of functions to choice sequences (Brouwer's principle)
- CHAPTER II. VARIOUS NOTIONS OF REALIZABILITY
- 8. Definition of realizability
- 9. Realizability under deduction in the intuitionistic formal system
- 10. Special realizability
- 11. Special realizability under deduction in the intuitionistic formal system
- CHAPTER III. THE INTUITIONISTIC CONTINUUM
- 12. Introduction
- 13. Real number generators and real numbers
- 14. The spread representation
- basic properties of the continuum
- 15. The uniform continuity theorem
- 16. The structure of the continuum
- CHAPTER IV. ON ORDER IN THE CONTINUUM
- 17. Introduction and preliminaries
- 18. Refutation, or proof of independence, of certain classical order properties
- BIBLIOGRAPHY
- SYMBOLS AND NOTATIONS
- INDEX
