内容

目次

Introduction; Part I. Ultraproducts in Analysis: 1. Introduction; 2.Normed space structures; 3. Signatures; 4. Ultrapowers of normed spacestructures; 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. Alternativeformulations of the theory; 12. Homogeneous structures; 13. More modeltheory; 14. Types; References; Index; Part II. Actions of Polish Groups andClassification Problems: 1. Introduction; 2. The general Glimm-Effrosdichotomy; 3. Actions of polish groups; 4. Actions of countable groups; 5.Actions of locally compact groups; 6. Actions of the infinite symmetricgroup; 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. OnSubspaces, Asymptotic Structure, and Distortion of Banach Spaces; Connectionswith 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. Aymptoticstructure; 7. Ordinal indices; 8. The homogeneous Banach space problem; 9.Concluding remarks; References; Index.