- 112 pages
- English
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Applications of Model Theory to Functional Analysis
About This Book
"The text is well written and easy to read. A great tool for any person interested in learning relations between functional analysis and model theory." ā MathSciNet
During the last two decades, methods that originated within mathematical logic have exhibited powerful applications to Banach space theory, particularly set theory and model theory. This volume constitutes the first self-contained introduction to techniques of model theory in Banach space theory. The area of research has grown rapidly since this monograph's first appearance, but much of this material is still not readily available elsewhere. For instance, this volume offers a unified presentation of Krivine's theorem and the Krivine-Maurey theorem on stable Banach spaces, with emphasis on the connection between these results and basic model-theoretic notions such as types, indiscernible sequences, and ordinal ranks.
Suitable for advanced undergraduates and graduate students of mathematics, this exposition does not presuppose expertise in either model theory or Banach space theory. Numerous exercises and historical notes supplement the text.
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CHAPTER 1
Preliminaries: Banach Space Models
1. Banach Space Structures and Banach Space Ultrapowers
Table of contents
- Cover
- Title Page
- Copyright Page
- Contents
- Chapter 0. Introduction
- Chapter 1. Preliminaries: Banach Space Models
- Chapter 2. Semidefinability of Types
- Chapter 3. Maurey Strong Types and Convolutions
- Chapter 4. Fundamental Sequences
- Chapter 5. Quantifier-Free Types Over Banach Spaces
- Chapter 6. Digression: Ramseyās Theorem for Analysis
- Chapter 7. Spreading Models
- Chapter 8. lp- and c0-Types
- Chapter 9. Extensions of Operators by Ultrapowers
- Chapter 10. Where Does the Number p Come From?
- Chapter 11. Block Representability of lp in Types
- Chapter 12. Krivineās Theorem
- Chapter 13. Stable Banach Spaces
- Chapter 14. Block Representability of lp in Types Over Stable Spaces
- Chapter 15. lp-Subspaces of Stable Banach Spaces
- Historical Remarks
- Bibliography
- Index of Notation
- Index