C. Ward Henson, José Iovino, Alexander S. Kechris

Analysis and Logic

• Broschiertes Buch

Produktbeschreibung

This volume comprises articles from four outstanding researchers who work at the cusp of analysis and logic. The emphasis is on active research topics; many results are presented that have not been published before and open problems are formulated. Considerable effort has been made by the authors to integrate their articles and make them accessible to mathematicians new to the area.

Table of contents:
Introduction; Part I. Ultraproducts in Analysis: 1. Introduction; 2. Normed space structures; 3. Signatures; 4. Ultrapowers of normed space structures; 5. Positive bounded formulas; 6. Basic model theory; 7. Quantifier-free formulas; 8. Ultraproducts of normed space structures; 9. Basic model theory II; 10. Isomorphic ultrapowers; 11. Alternative formulations of the theory; 12. Homogeneous structures; 13. More model theory; 14. Types; References; Index; Part II. Actions of Polish Groups and Classification Problems: 1. Introduction; 2. The general Glimm-Effros dichotomy; 3. Actions of polish groups; 4. Actions of countable groups; 5. Actions of locally compact groups; 6. Actions of the infinite symmetric group; 7. Turbulence I: overview; 8. Turbulence II: basic facts; 9. Turbulence III: induced actions; 10. Turbulence IV: some examples; 11. Turbulence V: calmness; 12. Turbulence VI: the first main theorem; 13. Turbulence VII: the second main theorem; References; Index; Part III. On Subspaces, Asymptotic Structure, and Distortion of Banach Spaces; Connections with Logic: 1. Introduction; 2. Background material: the 60's and 70's; 3. The unconditional basic sequence problem and connections with distortion; 4. Gowers' dichotomy: a block Ramsey theorem; 5. Distortion; 6. Aymptotic structure; 7. Ordinal indices; 8. The homogeneous Banach space problem; 9. Concluding remarks; References; Index.

This volume comprises articles from four outstanding researchers who work at the cusp of analysis and logic. The emphasis is on active research topics; many results are presented that have not been published before and open problems are formulated.

Articles from four outstanding researchers who work at the cusp of analysis and logic.

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Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.

Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 284
• Erscheinungstermin: 9. Dezember 2015
• Englisch
• Abmessung: 229mm x 152mm x 17mm
• Gewicht: 465g
• ISBN-13: 9780521648615
• ISBN-10: 0521648610
• Artikelnr.: 21348652

Inhaltsangabe

Introduction
Part I. Ultraproducts in Analysis: 1. Introduction
2. Normed space structures
3. Signatures
4. Ultrapowers of normed space structures
5. Positive bounded formulas
6. Basic model theory
7. Quantifier-free formulas
8. Ultraproducts of normed space structures
9. Basic model theory II
10. Isomorphic ultrapowers
11. Alternative formulations of the theory
12. Homogeneous structures
13. More model theory
14. Types
References
Index
Part II. Actions of Polish Groups and Classification Problems: 1. Introduction
2. The general Glimm-Effros dichotomy
3. Actions of polish groups
4. Actions of countable groups
5. Actions of locally compact groups
6. Actions of the infinite symmetric group
7. Turbulence I: overview
8. Turbulence II: basic facts
9. Turbulence III: induced actions
10. Turbulence IV: some examples
11. Turbulence V: calmness
12. Turbulence VI: the first main theorem
13. Turbulence VII: the second main theorem
References
Index
Part III. On Subspaces, Asymptotic Structure, and Distortion of Banach Spaces
Connections with Logic: 1. Introduction
2. Background material: the 60's and 70's
3. The unconditional basic sequence problem and connections with distortion
4. Gowers' dichotomy: a block Ramsey theorem
5. Distortion
6. Aymptotic structure
7. Ordinal indices
8. The homogeneous Banach space problem
9. Concluding remarks
References
Index.