## 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is the first of a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics, and discussion of research developments since the publication of the original volumes.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