Games, Scales and Suslin Cardinals
Alexander S. Kechris, Benedikt Löwe, John R. Steel, editors
Year: available September 2008
ISBN-13:9780521899512
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is the first of a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics, and discussion of research developments since the publication of the original volumes.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