Combinatory Logic
Published on 14. May 2014
435 pages
978-0-08-095742-5 (ISBN)
Description
Provability, Computability and Reflection
More details
Other editions
Additional editions
Lev D. Beklemishev
Provability, Computability and Reflection: Volume 22
Book
04/2000
Elsevier
€210.46
Article exhausted; check different version
Content
- Front Cover
- Combinatory Logic, Volume 22
- Copyright Page
- Table of Contents
- Preface
- Explanation of Notations
- Introduction
- A. The Analysis of Substitution
- B. The Russell Paradox
- C. Plan of the Work
- D. Historical Sketch
- Chapter 1. Formal Systems
- A. The Approach to Formal Systems
- B. Definition of a Formal System
- C. Philosophy of Formal Systems
- D. Linguistic Aspects of a Formal System
- E. Special Forms of Formal Systems
- S. Supplementary Topics
- Chapter 2. Epitheory
- A. The Nature of Epitheory
- B. Techniques of Induction
- C. Variables
- D. Replacement and Monotone Relations
- E. Theory of Definition
- S. Supplementary Topics
- Chapter 3. Lambda-Conversion
- A. Variables and Functions in Mathematics
- B. Functional Abstraction
- C. Morphology of a Formal ?-Applicative System
- D. Theoretical Rules of the Calculuses of Lambda-Conversion
- E. Substitution Prefixes
- S. Supplementary Topics
- Chapter 4. The Church-Rosser Theorem
- A. General Formulation
- B. Property (D)
- C. Property (E)
- D. Extension to Include ?-Conversion
- E. The Second Church-Rosser Theorem
- F. Theorems on Order
- S. Supplementary Topics
- Chapter 5. Intuitive Theory of Combinators
- A. Preliminary Discussion
- B. Interdefinability of Simple Combinators
- C. Terminology and Notation
- D. Properties of B
- E. Combinators Related to S
- F. Theorems on Order of Combinators
- G. Paradoxical Combinators
- H. Definitional Independence of Combinators
- S. Supplementary Topics
- Chapter 6. Synthetic Theory of Combinators
- A. Analysis of Combinatorial Completeness
- B. Basic Properties of H
- C. The Combinatory Axioms
- D. Theory of the Substitution Prefix
- E. Equivalence of H and Lambda-Conversion
- F. Theory of Strong Reduction
- S. Supplementary Topics
- Chapter 7. Logistic Foundations
- A. Preliminaries
- B. The Combinatory Rules
- C. The Systems 2
- D. The Systems K
- E. Modifications and Generalizations
- S. Supplementary Topics
- Chapter 8. Introduction to Illative Combinatory Logic
- A. The Russell Paradox
- B. Alternative Explanations of the Paradox
- C. The Notion of Functionality
- D. Relations to Other Illative Concepts
- E. Formal Preliminaries
- S. Supplementary Topics
- Chapter 9. The Basic Theory of Functionality
- A. Preliminaries
- B. The Subject-Construction Theorem
- C. Thc Subject-Conversion Theorems
- D. The Stratification Theorem and Its Consequences
- E. Analogies with Propositional Algebra
- F. Inferential Forms of Functionality
- S. Supplementary Topics
- Chapter 10. The Stronger Theories of Functionality
- A. Preliminaries
- B. General Properties of Deductions
- C. FR-Deductions
- D. The Restricted Theories
- E. Finite Formulation
- Appendix A. List of Basic Constants
- Appendix B. List of Properties of Relations
- Bibliography
- Index
