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The Cabal Seminar

The Cabal Seminar
Volumes I–IV
4 Volume Hardback Set

$325.00 (C)

Part of Lecture Notes in Logic

John R. Steel, Alexander S. Kechris, Yiannis N. Moschovakis, Itay Neeman, Donald A. Martin, Steve Jackson, Eugene M. Kleinberg, W. Hugh Woodin, Alessandro Andretta, Alain Louveau, Robert Van Wesep, Jean Saint-Raymond, Robert M. Solovay, Howard S. Becker, William W. Wadge, Leo A. Harrington, Theodore A. Slaman, Phokion G. Kolaitis, Piergiorgio Odifreddi, Andrew Marks, Paul B. Larson, Ilijas Farah, Claude Dellacherie, Matthew Foreman, Andrés Eduardo Caicedo, Benedikt Löwe
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  • Date Published: November 2020
  • availability: In stock
  • format: Multiple copy pack
  • isbn: 9781108920223

$ 325.00 (C)
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About the Authors
  • The proceedings of the Los Angeles Caltech-UCLA 'Cabal Seminar' were originally published in the 1970s and 1980s. This series of four books collects the seminal papers from those proceedings, together with extensive unpublished material, new papers on related topics, and discussion of research developments since the publication of the original volumes. Volume I focuses on the subjects of 'Games and Scales' and 'Suslin Cardinals, Partition Properties, and Homogeneity', Volume II on 'Wadge Degrees and Pointclasses' and 'Projective Ordinals', Volume III on 'HOD and its Local Versions' and 'Recursion Theory', and Volume IV on 'Extensions of AD, models with choice', along with material important to the Cabal that does not fit neatly into one of its main themes. These four volumes will be a necessary part of every set theorist's library.

    • Includes updated/revised material from the original Cabal Seminars volume
    • New, unpublished survey articles put the historical papers into context
    • Now includes uniform and modern notation to make the material more accessible to the reader
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    Product details

    • Date Published: November 2020
    • format: Multiple copy pack
    • isbn: 9781108920223
    • length: 1875 pages
    • dimensions: 230 x 155 x 130 mm
    • weight: 2.4kg
    • contains: 34 b/w illus. 2 tables
    • availability: In stock
  • Table of Contents

    Volume I: Part I. Games and Scales: Introduction to Part I
    1. Notes on the theory of scales
    2. Propagation of the scale property using games
    3. Scales on $\sum_1^1$-sets
    4. Inductive scales on inductive sets
    5. The extent of scales in $\mathbf{L}(\mathbb{R})$
    6. The largest countable this, that, and the other
    7. Scales in $\mathbf{L}(\mathbb{R})$
    8. Scales in $\mathbf{K}(\mathbb{R})$
    9. The real game quantifier propagates scales
    10. Long games
    11. The length-$\omega_1$ open game quantifier propagates scales
    Part II. Suslin Cardinals, Partition Properties, Homogeneity: Introduction to Part II
    12. Suslin cardinals, $\kappa$-Suslin sets, and the scale property in the hyperprojective hierarchy
    13. The axiom of determinacy, strong partition properties, and nonsingular measures
    14. The equivalence of partition properties and determinacy
    15. Generic codes for uncountable ordinals, partition properties, and elementary embeddings
    16. A coding theorem for measures
    17. The tree of a Moschovakis scale is homogeneous
    18. Weakly homogeneous trees
    Bibliography
    Volume II: Part III. Wadge Degrees and Pointclasses: Introduction to Part III
    19. Wadge degrees and descriptive set theory
    20. A note on Wadge degrees
    21. Some results in the Wadge hierarchy of Borel sets
    22. The strength of Borel Wadge determinacy
    23. Closure properties of pointclasses
    24. The axiom of determinacy and the prewellordering property
    25. Pointclasses and wellordered unions
    26. More closure properties of pointclasses
    27. More measures from AD
    28. Early investigations of the degress of Borel sets
    Part IV. Projective Ordinals: Introduction to Part IV
    29. Homogeneous trees and projective scales
    30. AD and projective ordinals
    31. A $\Delta_3^1$ coding of the subsets of $\omega_\omega$
    32. AD and projective ordinals
    33. Projective sets and cardinal numbers: some questions related to the continuum problem
    34. Regular cardinals without the weak partition property
    Bibliography
    Volume III: Part V. HOD and its Local Versions: Ordinal Definability in Models of Determinacy: Introduction to Part V
    35. Partially playful universes
    36. Ordinal games and playful models
    37. Measurable cardinals in playful models
    38. Introduction to Q-theory
    39. On the theory of $\prod_3^1$ sets of reals, II
    40. An inner models proof of the Kechris–Martin theorem
    41. A theorem of Woodin on mouse sets
    42. HOD as a core model
    Part VI. Recursion Theory: Recursion Theoretic Papers: Introduction to Part VI
    43. On recursion in E and semi-Spector classes
    44. On Spector classes
    45. Trees and degrees
    46. Definable functions on degrees
    47. $\prod_2^1$ monotone inductive definitions
    48. Martin's conjecture, arithmetic equivalence, and countable Borel equivalence relations
    Bibliography
    Volume IV: Part VII. Extensions of AD, Models with Choice: A Brief History of Determinacy
    49. 'AD plus uniformization' is equivalent to 'half $AD_\mathbb{R}$'
    50. The independence of DC from AD
    51. Games of countable length
    52. Some consistency results in ZFC using AD
    53. Subsets of $\aleph_1$ constructible from a real
    54. AD and the uniqueness of the supercompact measures on $\wp_{\omega_1}(\lambda)$
    55. The extender algebra and $\sum_1^2$-absoluteness
    Part VIII. Other Topics:
    56. On Vaught's conjecture
    57. Capacities and analytic sets
    58. More saturated ideals
    59. The fourteen Victoria Delfino problems and their status in the year 2020
    Bibliography.

  • Editors

    Alexander S. Kechris, California Institute of Technology
    Alexander S. Kechris is Professor of Mathematics at the California Institute of Technology. He is the recipient of numerous honors, including the J. S. Guggenheim Memorial Foundation Fellowship and the Carol Karp Prize of the Association for Symbolic Logic. He is also a member of the Scientific Research Board of the American Institute of Mathematics.

    Benedikt Löwe, Universiteit van Amsterdam
    Benedikt Löwe is Universitair Hoofddocent at the Universiteit van Amsterdam, Professor of Mathematics at the Universität Hamburg and Fellow of Churchill College at the University of Cambridge. He is currently the president of the Deutsche Vereinigung für Mathematische Logik und für Grundlagenforschung der Exakten Wissenschaften (DVMLG) and the Secretary General of the Division for Logic, Methodology and Philosophy of Science and Technology (DLMPST).

    John R. Steel, University of California, Berkeley
    John R. Steel is Professor of Mathematics at the University of California, Berkeley. Prior to that, he was a professor in the mathematics department at the University of California, Los Angeles. He is a recipient of the Carol Karp Prize of the Association for Symbolic Logic and of a Humboldt Prize. Steel is also a former Fellow at the Wissenschaftskolleg zu Berlin and the Sloan Foundation.

    Contributors

    John R. Steel, Alexander S. Kechris, Yiannis N. Moschovakis, Itay Neeman, Donald A. Martin, Steve Jackson, Eugene M. Kleinberg, W. Hugh Woodin, Alessandro Andretta, Alain Louveau, Robert Van Wesep, Jean Saint-Raymond, Robert M. Solovay, Howard S. Becker, William W. Wadge, Leo A. Harrington, Theodore A. Slaman, Phokion G. Kolaitis, Piergiorgio Odifreddi, Andrew Marks, Paul B. Larson, Ilijas Farah, Claude Dellacherie, Matthew Foreman, Andrés Eduardo Caicedo, Benedikt Löwe

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