Intuitionistic Logic, Model Theory and Forcing
Published on 14. May 2014
193 pages
978-0-08-095773-9 (ISBN)
Description
Intuitionistic Logic Model Theory and Forcing
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Lev D. Beklemishev
Provability, Computability and Reflection: Volume 54
Book
04/2000
Elsevier
€210.46
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Content
- Front Cover
- Intuitionistic Logic Model Theory and Forcing
- Copyright Page
- Contents
- Acknowledgments
- Introduction
- PART I: LOGIC
- Chapter 1. Propositional intuitionistic logic. semantics
- § 1. Formulas
- § 2. Models and validity
- § 3. Motivation
- § 4. Some properties of models
- § 5. Algebraic models
- § 6. Equivalence of algebraic and Kripke validity
- Chapter 2. Propositional intuitionistic logic. proof theory
- § 1. Beth tableaus
- § 2. Correctness of Beth tableaus
- § 3. Hintikka collections
- § 4. Completeness of Beth tableaus
- § 5. Examples
- Chapter 3. Related systems of logic
- § 1. ƒ-primitive intuitionistic logic. semantics
- § 2. ƒ-primitive intuitionistic logic. proof theory
- § 3. Minimal logic
- § 4. Classical logic
- § 5. Modal logic, S4
- semantics
- § 6. Modal logic. S4
- proof theory
- § 7. S4 and intuitionistic logic
- Chapter 4. First order intuitionistic logic. semantics
- § 1. Formulas
- § 2. Models and validity
- § 3. Motivation
- § 4. Some properties of models
- § 5. Examples
- § 6. Truth and almost-truth sets
- § 7. Complete sequences
- § 8. A connection with classical logic
- Chapter 5. First order intuitionistic logic. proof theory
- § 1. Beth tableaus
- § 2. Correctness of Beth tableaus
- § 3. Hintikka collections
- § 4. Hintikka elements
- § 5. Completeness of Beth tableaus
- § 6. Second completeness proof for Beth tableaus
- § 7. An axiom system, A1
- § 8. A second axiom system. A2
- § 9. Correctness of the system A2
- § 10. Completeness of the system A1
- Chapter 6. Additional fist order results
- § 1. Compactness
- § 2. Concerning the excluded middle law
- § 3. Skolem-Löwenheim
- § 4. Kleene tableaus
- § 5. Craig interpolation lemma
- § 6. Models with constant B function
- PART II: SET THEORY
- Chapter 7. Intuitionistic Ma generalizations
- § 1. Introduction
- § 2. The classical Ma sequence
- § 3. The intuitionistic Ma sequence
- § 4. Dominance
- § 5. A little about equality
- § 6. Weak substitutivity of equality
- § 7. More on dominance
- § 8. Axiom of extensionality
- § 9. Null set axiom
- § 10. Unordered pairs axiom
- § 11. Union axiom
- § 12. Axiom of infinity
- § 13. Axiom of regularity
- § 14. Definability of the models
- § 15. Power set axiom
- § 16. X-equivalence
- § 17. Axiom of substitution
- Chapter 8. Independence of the axiom of choice
- § 1. The specific model
- § 2. Symmetries
- § 3. Functions
- § 4. Axiom of choice
- Chapter 9. Ordinals and cardinals
- § 1. Definitions
- § 2. Some properties of ordinals
- § 3. General ordinal representatives
- § 4. Canonical ordinal representatives
- § 5. Ordinalized models
- § 6. Properties of ordinal representatives
- § 7. Types of ordinals
- § 8. Cardinalized models
- § 9. Countably incompatible G
- Chapter 10. Independence of the continuum hypothesis
- § 1. The specific model
- § 2. Countable incompatibility of W
- § 3. Cardinals and W
- § 4. Continuum hypothesis
- Chapter 11. Definability and constructability
- § 1.Definitions
- § 2. Adequacy of the definability formula
- § 3. ?-dominance
- § 4. The Ma sequence
- § 5 . Representatives of constructable sets
- § 6. Properties of constructable set representatives
- § 7. The principal result
- Chapter 12. Independence of the axiom of constructability
- § 1. The specific model
- § 2. Axiom of constructability
- Chapter 13. Additional results
- § 1. La representatives
- § 2. Definition functions
- § 3. Restriction on ordinals representable
- § 4. A classical connection
- § 5. Sets which are models
- § 6. Restriction on cardinals representable
- § 7. Axiom of choice
- § 8. Continuum hypothesis
- § 9. Classical counter models
- Chapter 14. Additional classical model generalizations
- § 1. Introduction
- § 2. Boolean valued logics
- § 3. Boolean valued Ra generalizations
- § 4. Intuitionistic Ra generalizations
- § 5. &G, R , ., Rg& is an intuitionistic ZF model
- § 6. Equivalence of the Ra generalizations
- § 7. Boolean valued Ma generalizations
- § 8. Equivalence of the Ma generalizations
- Appendix. to ch. 11 § 2
- § 1. Corresponding formulas
- § 2. Completeness of the definability formula
- § 3. Adequacy of the definability formula
- Bibliography
- Subject Index
