Games, Scales and Suslin Cardinals
The Cabal Seminar, Volume I

Presents seminal papers from the Caltech-UCLA 'Cabal Seminar', unpublished material, and related new papers.

Alexander S. Kechris (Edited by), Benedikt Löwe (Edited by), John R. Steel (Edited by)

9780521899512, Cambridge University Press

Hardback, published 15 September 2008

460 pages
23.6 x 15.8 x 3.2 cm, 0.74 kg

'… beautifully typed … quite different from a mere reprint of the previous Lecture Notes. Instead, the material is carefully organised so that it may serve as an advanced textbook equally well as a monograph on descriptive set theory.' EMS Newsletter

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is the first of a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics, and discussion of research developments since the publication of the original volumes.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

Part I. Games and Scales: 1. Games and scales
Introduction to Part I John R. Steel
2. Notes on the theory of scales Alexander S. Kechris and Yiannis N. Moschovakis
3. Propagation of the scale property using games Itay Neeman
4. Scales on E-sets John R. Steel
5. Inductive scales on inductive sets Yiannis N. Moschovakis
6. The extent of scales in L(R) Donald A. Martin and John R. Steel
7. The largest countable this, that, and the other Donald A. Martin
8. Scales in L(R) John R. Steel
9. Scales in K(R) John R. Steel
10. The real game quantifier propagates scales Donald A. Martin
11. Long games John R. Steel
12. The length-w1 open game quantifier propagates scales John R. Steel
Part II. Suslin Cardinals, Partition Properties, Homogeneity: 13. Suslin cardinals, partition properties, homogeneity
Introduction to Part II Steve Jackson
14. Suslin cardinals, K-suslin sets and the scale property in the hyperprojective hierarchy Alexander S. Kechris
15. The axiom of determinacy, strong partition properties and nonsingular measures Alexander S. Kechris, Eugene M. Kleinberg, Yiannis N. Moschovakis and W. Hugh Woodin
16. The equivalence of partition properties and determinacy Alexander S. Kechris
17. Generic codes for uncountable ordinals, partition properties, and elementary embeddings Alexander S. Kechris and W. Hugh Woodin
18. A coding theorem for measures Alexander S. Kechris
19. The tree of a Moschovakis scale is homogeneous Donald A. Martin and John R. Steel
20. Weakly homogeneous trees Donald A. Martin and W. Hugh Woodin.

Subject Areas: Game theory [PBUD], Mathematical logic [PBCD]