# The Cabal SeminarVolumes I–IV4 Volume Hardback Set

## $325.00 (C) Part of Lecture Notes in Logic John R. Steel, Alexander S. Kechris, Yiannis N. Moschovakis, Itay Neeman, Donald A. Martin, Steve Jackson, Eugene M. Kleinberg, W. Hugh Woodin, Alessandro Andretta, Alain Louveau, Robert Van Wesep, Jean Saint-Raymond, Robert M. Solovay, Howard S. Becker, William W. Wadge, Leo A. Harrington, Theodore A. Slaman, Phokion G. Kolaitis, Piergiorgio Odifreddi, Andrew Marks, Paul B. Larson, Ilijas Farah, Claude Dellacherie, Matthew Foreman, Andrés Eduardo Caicedo, Benedikt Löwe View all contributors • Date Published: November 2020 • availability: In stock • format: Multiple copy pack • isbn: 9781108920223 ##$325.00 (C) Multiple copy pack

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• The proceedings of the Los Angeles Caltech-UCLA 'Cabal Seminar' were originally published in the 1970s and 1980s. This series of four books collects the seminal papers from those proceedings, together with extensive unpublished material, new papers on related topics, and discussion of research developments since the publication of the original volumes. Volume I focuses on the subjects of 'Games and Scales' and 'Suslin Cardinals, Partition Properties, and Homogeneity', Volume II on 'Wadge Degrees and Pointclasses' and 'Projective Ordinals', Volume III on 'HOD and its Local Versions' and 'Recursion Theory', and Volume IV on 'Extensions of AD, models with choice', along with material important to the Cabal that does not fit neatly into one of its main themes. These four volumes will be a necessary part of every set theorist's library.

• Includes updated/revised material from the original Cabal Seminars volume
• New, unpublished survey articles put the historical papers into context
• Now includes uniform and modern notation to make the material more accessible to the reader

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## Product details

• Date Published: November 2020
• format: Multiple copy pack
• isbn: 9781108920223
• length: 1875 pages
• dimensions: 230 x 155 x 130 mm
• weight: 2.4kg
• contains: 34 b/w illus. 2 tables
• availability: In stock

Volume I: Part I. Games and Scales: Introduction to Part I
1. Notes on the theory of scales
2. Propagation of the scale property using games
3. Scales on $\sum_1^1$-sets
4. Inductive scales on inductive sets
5. The extent of scales in $\mathbf{L}(\mathbb{R})$
6. The largest countable this, that, and the other
7. Scales in $\mathbf{L}(\mathbb{R})$
8. Scales in $\mathbf{K}(\mathbb{R})$
9. The real game quantifier propagates scales
10. Long games
11. The length-$\omega_1$ open game quantifier propagates scales
Part II. Suslin Cardinals, Partition Properties, Homogeneity: Introduction to Part II
12. Suslin cardinals, $\kappa$-Suslin sets, and the scale property in the hyperprojective hierarchy
13. The axiom of determinacy, strong partition properties, and nonsingular measures
14. The equivalence of partition properties and determinacy
15. Generic codes for uncountable ordinals, partition properties, and elementary embeddings
16. A coding theorem for measures
17. The tree of a Moschovakis scale is homogeneous
18. Weakly homogeneous trees
Bibliography
Volume II: Part III. Wadge Degrees and Pointclasses: Introduction to Part III
19. Wadge degrees and descriptive set theory
20. A note on Wadge degrees
21. Some results in the Wadge hierarchy of Borel sets
22. The strength of Borel Wadge determinacy
23. Closure properties of pointclasses
24. The axiom of determinacy and the prewellordering property
25. Pointclasses and wellordered unions
26. More closure properties of pointclasses
27. More measures from AD
28. Early investigations of the degress of Borel sets
Part IV. Projective Ordinals: Introduction to Part IV
29. Homogeneous trees and projective scales
30. AD and projective ordinals
31. A $\Delta_3^1$ coding of the subsets of $\omega_\omega$
32. AD and projective ordinals
33. Projective sets and cardinal numbers: some questions related to the continuum problem
34. Regular cardinals without the weak partition property
Bibliography
Volume III: Part V. HOD and its Local Versions: Ordinal Definability in Models of Determinacy: Introduction to Part V
35. Partially playful universes
36. Ordinal games and playful models
37. Measurable cardinals in playful models
38. Introduction to Q-theory
39. On the theory of $\prod_3^1$ sets of reals, II
40. An inner models proof of the Kechris–Martin theorem
41. A theorem of Woodin on mouse sets
42. HOD as a core model
Part VI. Recursion Theory: Recursion Theoretic Papers: Introduction to Part VI
43. On recursion in E and semi-Spector classes
44. On Spector classes
45. Trees and degrees
46. Definable functions on degrees
47. $\prod_2^1$ monotone inductive definitions
48. Martin's conjecture, arithmetic equivalence, and countable Borel equivalence relations
Bibliography
Volume IV: Part VII. Extensions of AD, Models with Choice: A Brief History of Determinacy
49. 'AD plus uniformization' is equivalent to 'half $AD_\mathbb{R}$'
50. The independence of DC from AD
51. Games of countable length
52. Some consistency results in ZFC using AD
53. Subsets of $\aleph_1$ constructible from a real
54. AD and the uniqueness of the supercompact measures on $\wp_{\omega_1}(\lambda)$
55. The extender algebra and $\sum_1^2$-absoluteness
Part VIII. Other Topics:
56. On Vaught's conjecture
57. Capacities and analytic sets
58. More saturated ideals
59. The fourteen Victoria Delfino problems and their status in the year 2020
Bibliography.

• ## 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. He is also a member of the Scientific Research Board of the American Institute of Mathematics.

Benedikt Löwe, Universiteit van Amsterdam
Benedikt Löwe is Universitair Hoofddocent at the Universiteit van Amsterdam, Professor of Mathematics at the Universität Hamburg and Fellow of Churchill College at the University of Cambridge. He is currently the president of the Deutsche Vereinigung für Mathematische Logik und für Grundlagenforschung der Exakten Wissenschaften (DVMLG) and the Secretary General of the Division for Logic, Methodology and Philosophy of Science and Technology (DLMPST).

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 the University of California, Los Angeles. He is a recipient of the Carol Karp Prize of the Association for Symbolic Logic and of a Humboldt Prize. Steel is also 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, Alessandro Andretta, Alain Louveau, Robert Van Wesep, Jean Saint-Raymond, Robert M. Solovay, Howard S. Becker, William W. Wadge, Leo A. Harrington, Theodore A. Slaman, Phokion G. Kolaitis, Piergiorgio Odifreddi, Andrew Marks, Paul B. Larson, Ilijas Farah, Claude Dellacherie, Matthew Foreman, Andrés Eduardo Caicedo, Benedikt Löwe

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