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Analysis and Logic

Analysis and Logic


Part of London Mathematical Society Lecture Note Series

  • Date Published: March 2003
  • availability: Available
  • format: Paperback
  • isbn: 9780521648615

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About the Authors
  • 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
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    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

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    Product details

    • Date Published: March 2003
    • format: Paperback
    • isbn: 9780521648615
    • length: 284 pages
    • dimensions: 229 x 153 x 20 mm
    • weight: 0.42kg
    • availability: Available
  • Table of Contents

    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
    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
    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

  • Authors

    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

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