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Cabal Seminar 4 Volume Hardback Set: Volumes IIV [Multiple-component retail product]

Edited by (Universiteit van Amsterdam), Edited by (University of California, Berkeley), Edited by (California Institute of Technology)
  • Formaat: Multiple-component retail product, 1875 pages, kõrgus x laius x paksus: 230x155x130 mm, kaal: 2400 g, Worked examples or Exercises; 2 Tables, black and white; 10 Halftones, black and white; 24 Line drawings, black and white, Contains 4 hardbacks
  • Sari: Lecture Notes in Logic
  • Ilmumisaeg: 12-Nov-2020
  • Kirjastus: Cambridge University Press
  • ISBN-10: 1108920225
  • ISBN-13: 9781108920223
  • Formaat: Multiple-component retail product, 1875 pages, kõrgus x laius x paksus: 230x155x130 mm, kaal: 2400 g, Worked examples or Exercises; 2 Tables, black and white; 10 Halftones, black and white; 24 Line drawings, black and white, Contains 4 hardbacks
  • Sari: Lecture Notes in Logic
  • Ilmumisaeg: 12-Nov-2020
  • Kirjastus: Cambridge University Press
  • ISBN-10: 1108920225
  • ISBN-13: 9781108920223
This series of four books presents the seminal papers from the Caltech-UCLA 'Cabal Seminar' together with extensive unpublished material, new papers on related topics, and discussion of research developments since the publication of the original volumes.

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 This series of four books collects the seminal papers from those proceedings, together with extensive unpublished material, new papers on related topics, and discussion of research developments since the publication of the original volumes.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.

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A collection of four books presenting the seminal papers from the Caltech-UCLA 'Cabal Seminar'.
Preface ix
PART I GAMES AND SCALES
Games and scales. Introduction to Part I
3(25)
John R. Steel
Notes on the theory of scales
28(47)
Alexander S. Kechris
Yiannis N. Moschovakis
Propagation of the scale property using games
75(15)
Itay Neeman
Scales on Σ-sets
90(4)
John R. Steel
Inductive scales on inductive sets
94(8)
Yiannis N. Moschovakis
Scales on coinductive sets
102(8)
Yiannis N. Moschovakis
The extent of scales in L(R)
110(11)
Donald A. Martin
John R. Steel
The largest countable this. that, and the other
121(9)
Donald A. Martin
Scales in L(R)
130(46)
John R. Steel
Scales in K(R)
176(33)
John R. Steel
The real game quantifier propagates scales
209(14)
Donald A. Martin
Long games
223(37)
John R. Steel
The length-ω1 open game quantifier propagates scales
260(13)
John R. Steel
PART II SUSLIN CARDINALS, PARTITION PROPERTIES, HOMOGENEITY
Suslin cardinals, partition properties, homogeneity. Introduction to Part II
273(41)
Steve Jackson
Suslin cardinals, κ-Suslin sets, and the scale property in the hyperprojective hierarchy
314(19)
Alexander S. Kechris
The axiom of determinacy, strong partition properties, and nonsingular measures
333(22)
Alexander S. Kechris
Eugene M. Kleinberg
Yiannis N. Moschovakis
W. Hugh Woodin
The equivalence of partition properties and determinacy
355(24)
Alexander S. Kechris
W. Hugh Woodin
Generic codes for uncountable ordinals, partition properties, and elementary embeddings
379(19)
Alexander S. Kechris
W. Hugh Woodin
A coding theorem for measures
398(6)
Alexander S. Kechris
The tree of a Moschovakis scale is homogeneous
404(17)
Donald A. Martin
John R. Steel
Weakly homogeneous trees
421(18)
Donald A. Martin
W. Hugh Woodin
Bibliography 439(80)
Preface ix
Original Numbering xiii
PART III WADGE DEGREES AND POINTCLASSES
Wadge degrees and pointclasses. Introduction to Part III
3(21)
Alessandro Andretta
Alain Louveau
Wadge degrees and descriptive set theory
24(19)
Robert Van Wesep
A note on Wadge degrees
43(4)
Alexander S. Kechris
Some results in the Wadge hierarchy of Borel sets
47(27)
Alain Louveau
The strength of Borel Wadge determinacy
74(28)
Alain Louveau
Jean Saint-Raymond
Closure properties of pointclasses
102(16)
John R. Steel
The axiom of determinacy and the prewellordering property
118(23)
Alexander S. Kechris
Robert M. Solovay
John R. Steel
Pointclasses and wellordered unions
141(13)
Steve Jackson
Donald A. Martin
More closure properties of pointclasses
154(6)
Howard S. Becker
More measures from AD
160(6)
John R. Steel
Early investigations of the degrees of Borel sets
166(33)
William W. Wadge
PART IV PROJECTIVE ORDINALS
Projective ordinals. Introduction to Part IV
199(71)
Steve Jackson
Homogeneous trees and projective scales
270(34)
Alexander S. Kechris
AD and projective ordinals
304(42)
Alexander S. Kechris
A Δ13 coding of the subsets of cam
346(18)
Robert M. Solovay
AD and the projective ordinals
364(120)
Steve Jackson
Projective sets and cardinal numbers: some questions related to the continuum problem
484(25)
Donald A. Martin
Regular cardinals without the weak partition property
509(10)
Steve Jackson
Bibliography 519(2)
Preface vii
Original Numbering xi
PART V HOD AND ITS LOCAL VERSIONS
Ordinal definability in models of determinacy. Introduction to Part V
3(46)
John R. Steel
Partially playful universes
49(37)
Howard S. Becker
Ordinal games and playful models
86(29)
Yiannis N. Moschovakis
Measurable cardinals in playful models
115(11)
Howard S. Becker
Yiannis N. Moschovakis
Introduction to Q-theory
126(74)
Alexander S. Kechris
Donald A. Martin
Robert M. Solovay
On the theory of Π13 sets of reals, II
200(20)
Alexander S. Kechris
Donald A. Martin
An inner models proof of the Kechris-Martin theorem
220(23)
Itay Neeman
A theorem of Woodin on mouse sets
243(14)
John R. Steel
HOD as a core model
257(92)
John R. Steel
W. Hugh Woodin
PART VI RECURSION THEORY
Recursion theoretic papers. Introduction to Part VI
349(6)
Leo A. Harrington
Theodore A. Slaman
On recursion in E and semi-Spector classes
355(35)
Phokion G. Kolaitis
On Spector classes
390(34)
Alexander S. Kechris
Trees and degrees
424(34)
Piergiorgio Odifreddi
Definable functions on degrees
458(18)
Theodore A. Slaman
John R. Steel
Π12 monotone inductive definitions
476(17)
Donald A. Martin
Martin's conjecture, arithmetic equivalence, and countable Borel equivalence relations
493(28)
Andrew Marks
Theodore A. Slaman
John R. Steel
Bibliography 521
Preface vii
Original Numbering xi
PART VII EXTENSIONS OF AD, MODELS WITH CHOICE
A brief history of determinacy
3(58)
Paul B. Larson
"AD plus Uniformization" is equivalent to "Half ADR"
61(5)
Alexander S. Kechris
The independence of DC from AD
66(30)
Robert M. Solovay
Games of countable length
96(8)
Donald A. Martin
Some consistency results in ZFC using AD
104(26)
W. Hugh Woodin
Subsets of ℵ1 constructible from a real
130(6)
Alexander S. Kechris
AD and the uniqueness of the supercompact measures on ω1 (λ)
136(5)
W. Hugh Woodin
The extender algebra and Sf-absoluteness
141(38)
Ilijas Farah
PART VIII OTHER TOPICS
On Vaught's conjecture
179(17)
John R. Steel
Capacities and analytic sets
196(27)
Claude Dellacherie
More saturated ideals
223(25)
Matthew Foreman
The fourteen Victoria Delfino problems and their status in the year 2020
248(33)
Andres Eduardo Caicedo
Benedikt Lowe
Bibliography 281
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 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 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.