Analysis and Logic

This volume comprises articles from four outstanding researchers who work at the cusp of analysis and logic.

C. Ward Henson (Author), José Iovino (Author), Alexander S. Kechris (Author), Edward Odell (Author), Catherine Finet (Edited by), Christian Michaux (Edited by)

9780521648615, Cambridge University Press

Paperback, published 13 January 2003

284 pages
22.9 x 15.3 x 2 cm, 0.42 kg

'One does not need to be a specialist in analysis to find this book a worthy item in the library.' European Mathematical Society Newsletter

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.

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.

Subject Areas: Calculus & mathematical analysis [PBK], Mathematical logic [PBCD]