Analysis and Logic
Analysis and Logic
C. Ward Henson, University of Illinois, Urbana-Champaign
José Iovino, University of Texas Health Science Center, San Antonio
Alexander S. Kechris, California Institute of Technology
Edward Odell, University of Texas, Austin
Catherine Finet
Christian Michaux
José Iovino, University of Texas Health Science Center, San Antonio
Alexander S. Kechris, California Institute of Technology
Edward Odell, University of Texas, Austin
Catherine Finet
Christian Michaux
May 2003
Paperback
9780521648615
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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.
- Many results are presented that have not been published before
- Exposition is clear and accessible to all mathematicians
- Excellent introduction to the current state of the art in infinite dimensional Banach space theory
Reviews & endorsements
'One does not need to be a specialist in analysis to find this book a worthy item in the library.' European Mathematical Society Newsletter
Product details
May 2003Paperback
9780521648615
284 pages
229 × 153 × 20 mm
0.42kg
Available
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.
