Analysis and Logic

C. Ward Henson, José Iovino, Alexander S. Kechris, Edward Odell (Autoren)

Buch | Softcover

284 Seiten

2003
Cambridge University Press (Verlag)
978-0-521-64861-5 (ISBN)

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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.

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.

Erscheint lt. Verlag	13.1.2003
Reihe/Serie	London Mathematical Society Lecture Note Series
Zusatzinfo	Worked examples or Exercises
Verlagsort	Cambridge
Sprache	englisch
Maße	153 x 229 mm
Gewicht	420 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
ISBN-10	0-521-64861-0 / 0521648610
ISBN-13	978-0-521-64861-5 / 9780521648615
Zustand	Neuware