Large Infinitary Languages

Name: Large Infinitary Languages | Model Theory
Brand: Elsevier
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Model Theory

M. A. Dickmann Lev D. Beklemishev(Autor*in)

Elsevier (Verlag)

Erschienen am 14. Mai 2014

481 Seiten

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Inhalt

Front Cover
Large Infinitary Languages: Model Theory
Copyright Page
Preface
Contents
Chapter 0. Preliminaries
§ 1. Set-theoretical background
§ 2. "Constructibly" defined inaccessible cardinals
§ 3. Filters and ultrafilters
ultraproducts
trees
§ 4. Measurable cardinals
§ 5. Partition calculus
Chapter 1. The Basic Notions of Infinitary Languages
§ 1. Elementary syntax and semantics of the language Lk?
§ 2. Examples
§ 3. Classification of formulas, model classes and maps
Chapter 2. Some Results From The Model Theory of L?? And L?1?
§ 1. Background on types and saturated structures
§ 2. Models generated by indiscernibles
§ 3. Some results from the model theory of L?1?
Chapter 3. General Results
§ 1. Incompactness of accessible cardinals
§ 2. Incompactness results for inaccessible cardinals
§ 3. Larger cardinals
§ 4.The downward Löwenheim-Skolem theorem
§ 5.The upward Lowenheim-Skolem theorem and generalizations
Hanf numbers
Morley numbers
Chapter 4. Infinitary Languages With Finite Quantifiers
§ 1. The Hanf number of L... and Morley numbers
§ 2. Lower bounds for Hanf and Morley numbers
§ 3. Omitting types
upper bounds for Morley numbers
§ 4. Applications: non-definability of well-orderings in L.,
§ 4. Applications: non-definability of well-orderings in Lk?
§ 5. Further Hanf number computations
Chapter 5. Languages with Infinite Quantifiers
§ 1. The Hanf number of languages with infinite quantifiers
§ 2. The language L?? for ? strongly inaccessible
§ 3. Extension of partial isomorphisms
§ 4. Applications of the back and forth method
Appendix A. Induction For Well-Founded Relations and The Shepherdson-Mostowski Theorem
Appendix B.an L?1?1 Formula With no Prenex Form
I. Some absoluteness notions and results
II. Construction of the formula
Appendix C. Axiomatizability, Completeness and Definability Results
I. A review of (positive) completeness and definability results for infinitary logic
II. Scott's undefinability theorem
Appendix D. Results on The Constructible Universe
Appendix E. Real-valued Measurable Cardinals and the Tree Property
References
Index
List of Symbols

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