Analysis and Logic

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

• ISBN13: 9780521648615
• ISBN10: 0521648610
• Format: Paperback
• Copyright: 2003-01-13
• Publisher: Cambridge University Press

Summary

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

Preface	ix
Introduction	xi
Ultraproducts in Analysis	1	(114)
C. Ward Henson
Jose Iovino
Introduction	3	(7)
Normed Space Structures	10	(3)
Signatures	13	(4)
Ultrapowers of Normed Space Structures	17	(4)
Positive Bounded Formulas	21	(10)
Basic Model Theory I	31	(3)
Quantifier-Free Formulas	34	(4)
Ultraproducts of Normed Space Structures	38	(5)
Basic Model Theory II	43	(12)
Isomorphic Ultrapowers	55	(17)
Alternative Formulations of the Theory	72	(3)
Homogeneous Structures	75	(4)
More Model Theory	79	(17)
Types	96	(19)
References	107	(4)
Index of Notation	111	(1)
Index	112	(3)
Actions of Polish Groups and Classification Problems	115	(74)
Alexander S. Kechris
Introduction	117	(3)
The General Glimm-Effros Dichotomy	120	(3)
Actions of Polish Groups	123	(3)
Actions of Countable Groups	126	(5)
Actions of Locally Compact Groups	131	(2)
Actions of the Infinite Symmetric Group	133	(4)
Turbulence I: Overview	137	(6)
Turbulence II: Basic Facts	143	(3)
Turbulence III: Induced Actions	146	(4)
Turbulence IV: Some Examples	150	(2)
Turbulence V: Calmness	152	(5)
Turbulence VI: The First Main Theorem	157	(6)
Turbulence VII: The Second Main Theorem	163	(26)
References	183	(3)
Index	186	(3)
On Subspaces, Asymptotic Structure, and Distortion of Banach Spaces; Connections with Logic	189
Edward Odell
Introduction	191
Background material: The 60's and 70's	194
The unconditional basic sequence problem and connections with distortion	208
Gowers' dichotomy: A block Ramsey Theorem	217
Distortion	223
Asymptotic structure	233
Ordinal Indices	244
The homogeneous Banach space problem	252
Concluding remarks	254
References	256
Index	265