Applications of model theory to functional analysis

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Title:

Author:

Iovino, José, author.

ISBN:

9780486780849

Personal Author:

Iovino, José, author.

Physical Description:

xii, 95 pages ; 22 cm.

Series:

Dover books on mathematics

Dover books on mathematics.

Contents:

Preliminaries: Banach space models -- Semidefinability of types -- Maurey strong types and convolutions -- Fundamental sequences -- Quantifier-free types over Banach spaces -- Digression: Ramsey's theorem for analysis -- Spreading models -- ℓp- and c₀ -types -- Extensions of operators by ultrapowers -- Where does the number p come from? -- Block representability of ℓp in types -- Krivine's theorem -- Stable Banach spaces -- Block representabiltiy of ℓp in types over stable spaces -- ℓp-subspaces of stable Banach spaces.

Subject Term:

Banach spaces.

Model theory.

Copies:

Available:*

Library	Material Type	Item Barcode	Shelf Number	Copy	Status
Searching... 1:IIEMSA	1:GEN-BOOK	33168025791670	515.732 I.64A 2014	1	Searching... Unknown

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Summary

""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."" - MathSciNetDuring 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.