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Look Inside Games, Scales and Suslin Cardinals

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

Part of Lecture Notes in Logic

Editors:
Alexander S. Kechris, California Institute of Technology
Benedikt Löwe, Universiteit van Amsterdam
John R. Steel, University of California, Berkeley

John R. Steel. Alexander S. Kechris, Yiannis N. Moschovakis, Itay Neeman, Donald A. Martin, Steve Jackson, Eugene M. Kleinberg, W. Hugh Woodin

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Date Published: December 2008
availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
format: Adobe eBook Reader
isbn: 9780511451416

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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. 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is the first of a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics, and discussion of research developments since the publication of the original volumes.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.
- Includes updated/revised material from original volume of Cabal Seminars
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Reviews & endorsements
'… 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

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Product details
- Date Published: December 2008
- format: Adobe eBook Reader
- isbn: 9780511451416
- availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
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.
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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, and is a member of the Scientific Research Board of the American Institute of Mathematics.
Benedikt Löwe, Universiteit van Amsterdam
Benedikt Löwe is Universitair Docent in Logic and Scientific Director of the Graduate Programme in Logic at the Institute for Logic, Language and Computation of the Universiteit van Amsterdam. He is an editor of the Journal of Logic, Language and Information and Managing Editor for the Tbilisi Mathematical Journal. He is a board member of the DVMLG and the EACSL.
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 UCLA. He is a recipient of the Carol Karp Prize of the Association for Symbolic Logic and of a Humboldt Prize. Steel is 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