Games, Scales and Suslin Cardinals

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 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 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.

• 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.

'… 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