UID:
almahu_9949697333502882
Format:
1 online resource (229 p.)
ISBN:
1-283-52572-0
,
9786613838179
,
0-08-095487-1
Series Statement:
Studies in logic and the foundations of mathematics ; v. 77
Content:
Provability, Computability and Reflection
Note:
Description based upon print version of record.
,
Front Cover; Elementary Induction on Abstract Structures; Copyright Page; Preface; CONTENTS; Introduction; Chapter 1. Positive elementary inductive deflnitions; 1A. Monotone operators; 1B. Relative positive inductive definability; 1C. Combining inductions; 1D. Inductive definability on a structure; Exercises; Chapter 2. The stages of an inductive definition; 2A. The Stage Comparison Theorem; 2B. Closure ordinals and the Closure Theorem; Exercises; Chapter 3. Structure theory for inductive relations; 3A. Inductive norms and the Prewellordering Theorem; 3B. Making hyperelementary selections
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3C. The Boundedness and Covering Theorems.3D. Expanding a structure by an inductive relation; 3E. Generalization of the theory to richer languages; Exercises; Chapter 4. Games and game quantifiers; 4A. Interpreting quantifier strings via games; 4B. A canonical form for positive formulas; 4C. Explicit formulas for inductive relations; Exercises; Chapter 5. Acceptable structures; 5A. Coding schemes; 5B. Satisfaction is hyperelementary; 5C. The quantifier G; 5D. Parametrizations and universal sets; Exercises; Chapter 6. Inductive second order relations
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6A. Relativization of inductive definitions examples; 6B. Transitivity, Substitutivity and Positive Induction Completeness; 6C. Extension of the theory to second order relations; 6D. The class of hyperelementary relations; Exercises; Chapter 7. Second order characterizations; 7A. Inductive and S1 1 relations; 7B. Quasistrategies; 7C. The Second Stage Comparison Theorem; 7D. The Abstract Spector-Gandy Theorem; 7E. The hierarchy of hyperelementary sets; 7F. Model theoretic characterizations; Exercises; Chapter 8. Countable acceptable structures; 8A. The Abstract Kleene Theorem
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8B. The Perfect Set Theorem8C. The intersection of U-models of second order comprehension; 8D. Counterexamples to special properties of arithmetic; the language L ?1,G; 8E. The Suslin-Kleene Theorem; Exercises; Chapter 9. The next admissible set; 9A. Spector classes of relations; 9B. Examples of Spector classes; 9C. Structure theory for Spector classes; 9D. Admissible sets; 9E. The companion of a Spector class; 9F. The next admissible set; Exercises; References; Index; Index of symbols
,
English
Additional Edition:
ISBN 0-444-10537-9
Language:
English
