UID:
almahu_9949697728802882
Format:
1 online resource (435 p.)
ISBN:
1-283-52622-0
,
9786613838674
,
0-08-095742-0
Series Statement:
Studies in logic and the foundations of mathematics ; v. 65
Content:
Provability, Computability and Reflection
Note:
Description based upon print version of record.
,
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
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E. Theory of DefinitionS. 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
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B. Interdefinability of Simple CombinatorsC. 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
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B. The Combinatory RulesC. 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
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F. Inferential Forms of FunctionalityS. 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
,
English
Additional Edition:
ISBN 0-444-53387-7
Language:
English
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