Lecture Notes in Logic, 31

Games, Scales and Suslin Cardinals

Alexander S. Kechris, Benedikt Löwe, John R. Steel, editors

Year: available September 2008

464 pages. Hardcover.
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The proceedings of the Los Angeles Caltech-UCLA “Cabal Seminar” were originally published in the 1970s and 1980s. Games, Scales, and Suslin Cardinals is the first of a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics, and discussion of research developments since the publication of the original volumes. Focusing on the subjects of “Games and Scales” (Part 1) and “Suslin Cardinals, Partition Properties, and Homogeneity” (Part 2), each of the two sections is preceded by an introductory survey putting the papers into present context. This volume will be an invaluable reference for anyone interested in higher set theory.

Table of Contents

Part I. Games and Scales:

  • John R. Steel
    Introduction to part I
  • Alexander S. Kechris, Yiannis N. Moschovakis
    Notes on the theory of scales
  • Itay Neeman
    Propagation of the scale property using games
  • John R. Steel
    Scales in E-sets
  • Yiannis N. Moschovakis
    Inductive scales on inductive sets
  • Donald A. Martin, John R. Steel
    The extent of scales in L(R)
  • Donald A. Martin
    The largest coutable this, that, and the other
  • John R. Steel
    Scales in L(R)
  • John R. Steel
    Scales in K(R)
  • Donald A. Martin
    The real game quantifier propagates scales
  • John R. Steel
    Long games
  • John R. Steel
    The length-w1 open game quantifier propagates scales

Part II. Suslin Cardinals, Partition Properties, Homogeneity:

  • Steve Jackson
    Introduction to Part II
  • Alexander S. Kechris
    Suslin cardinals, K-suslin sets and the scale property in the hyperprojective hierarchy
  • Alexander S. Kechris, Eugene M. Kleinberg, Yiannis N. Moschovakis, W. Hugh Woodin
    The axiom of determinacy, strong partition properties and nonsingular measures
  • Alexander S. Kechris
    The equivalence of partition properties and determinacy
  • Alexander S. Kechris and W. Hugh Woodn
    Generic codes for uncountable ordinals, partition properties, and elementary embeddings
  • Alexander S. Kechris
    A coding theorem for measures
  • Donald A. Martin, John R. Steel
    The tree of a Moschovakis scale is homogeneous
  • Donald A. Martin and W. Hugh Woodin
    Weakly homogeneous trees