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

doi:10.1017/CBO9780511546488

Games, Scales and Suslin Cardinals

The Cabal Seminar, Volume I

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Jackson, Steve 2011. Wadge Degrees and Projective Ordinals The Cabal Seminar Volume II. p. 509.

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Jackson, Steve and Martin, Donald A. 2011. Wadge Degrees and Projective Ordinals The Cabal Seminar Volume II. p. 141.

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Kechris, Alexander S. Solovay, Robert M. and Steel, John R. 2011. Wadge Degrees and Projective Ordinals The Cabal Seminar Volume II. p. 118.

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Kechris, Alexander S. 2011. Wadge Degrees and Projective Ordinals The Cabal Seminar Volume II. p. 270.

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Steel, John R. 2011. Wadge Degrees and Projective Ordinals The Cabal Seminar Volume II. p. 102.

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Steel, John R. 2011. Wadge Degrees and Projective Ordinals The Cabal Seminar Volume II. p. 160.

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Jackson, Steve 2011. Wadge Degrees and Projective Ordinals The Cabal Seminar Volume II. p. 199.

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Andretta, Alessandro and Louveau, Alain 2011. Wadge Degrees and Projective Ordinals The Cabal Seminar Volume II. p. 3.

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Apter, Arthur Jackson, Stephen and Löwe, Benedikt 2012. Cofinality and measurability of the first three uncountable cardinals. Transactions of the American Mathematical Society, Vol. 365, Issue. 1, p. 59.

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Cunningham, Daniel W. 2015. Strong partition cardinals and determinacy in $${K(\mathbb{R})}$$ K ( R ). Archive for Mathematical Logic, Vol. 54, Issue. 1-2, p. 173.

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Cunningham, Daniel W. 2017. A strong partition cardinal above $$\varTheta $$ Θ. Archive for Mathematical Logic, Vol. 56, Issue. 3-4, p. 403.

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SARGSYAN, GRIGOR and TRANG, NAM 2021. SEALING OF THE UNIVERSALLY BAIRE SETS. The Bulletin of Symbolic Logic, Vol. 27, Issue. 3, p. 254.

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Saveliev, Denis Igorevich 2022. О редукции и отделимости проективных множеств в тихоновских пространствах. Успехи математических наук, Vol. 77, Issue. 1(463), p. 189.

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Sargsyan, Grigor and Trang, Nam 2024. The exact consistency strength of the generic absoluteness for the universally Baire sets. Forum of Mathematics, Sigma, Vol. 12, Issue. ,

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

Publisher:: Cambridge University Press
Online publication date:: January 2010
Print publication year:: 2008
Online ISBN:: 9780511546488
DOI:: https://doi.org/10.1017/CBO9780511546488

Subjects:: Mathematics, Logic, Categories and Sets, Programming Languages and Applied Logic
Series:: Lecture Notes in Logic (31)

101.00 (GBP)

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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.

'… 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.'

Source: EMS Newsletter

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Games, Scales and Suslin Cardinals

The Cabal Seminar, Volume I

This Book has been cited by the following publications. This list is generated based on data provided by Crossref.

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Contents

Frontmatter
pp i-vi

Contents
pp vii-viii

Preface
pp ix-xi

PART I - GAMES AND SCALES
pp 1-2

Games and scales. Introduction to Part I
pp 3-27

Notes on the theory of scales
pp 28-74

Propagation of the scale property using games
pp 75-89

Scales on ∑11-sets
pp 90-93

Inductive scales on inductive sets
pp 94-101

Scales on coinductive sets
pp 102-109

The extent of scales in L(ℝ)
pp 110-120

The largest countable this, that, and the other
pp 121-129

Scales in L(ℝ)
pp 130-175

Scales in K(ℝ)
pp 176-208

The real game quantifier propagates scales
pp 209-222

Long games
pp 223-259

The length-ω1 open game quantifier propagates scales
pp 260-270

PART II - SUSLIN CARDINALS, PARTITION PROPERTIES, HOMOGENEITY
pp 271-272

Suslin cardinals, partition properties, homogeneity. Introduction to Part II
pp 273-313

Suslin cardinals, k-Suslin sets, and the scale property in the hyperprojective hierarchy
pp 314-332

The axiom of determinacy, strong partition properties, and nonsingular measures
pp 333-354

The equivalence of partition properties and determinacy
pp 355-378

Generic codes for uncountable ordinals, partition properties, and elementary embeddings
pp 379-397

A coding theorem for measures
pp 398-403

The tree of a Moschovakis scale is homogeneous
pp 404-420

Weakly homogeneous trees
pp 421-438

Bibliography
pp 439-445

Lecture Notes in Logic
pp 446-447

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Games, Scales and Suslin Cardinals

The Cabal Seminar, Volume I

Book description

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