Ordinal Definability and Recursion Theory: The Cabal Seminar, Volume III

doi:10.1017/CBO9781139519694

The proceedings of the Los Angeles Caltech-UCLA 'Cabal Seminar' were originally published in the 1970s and 1980s. Ordinal Definability and Recursion Theory is the third in a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics and discussion of research developments since the publication of the original volumes.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 'HOD and its Local Versions' (Part V) and 'Recursion Theory' (Part VI), each of the two sections is preceded by an introductory survey putting the papers into present context. These four volumes will be a necessary part of the book collection of every set theorist.

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Contents

Frontmatter
pp i-iv
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Contents
pp v-vi
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Preface
pp vii-x
- By Alexander S. Kechris, California Institute of Technology, Benedikt Löwe, Universiteit van Amsterdam, John R. Steel, University of California, Berkeley
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Original Numbering
pp xi-xvi
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PART V - HOD AND ITS LOCAL VERSIONS
pp 1-2
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Ordinal definability in models of determinacy. Introduction to Part V
pp 3-48
- By John R. Steel, University of California, Berkeley
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Partially playful universes
pp 49-85
- By Howard S. Becker
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Ordinal games and playful models
pp 86-114
- By Yiannis N. Moschovakis, UNIVERSITY OF CALIFORNIA LOS ANGELES
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Measurable cardinals in playful models
pp 115-125
- By Howard S. Becker, Yiannis N. Moschovakis, UNIVERSITY OF CALIFORNIA LOS ANGELES
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Introduction to Q-theory
pp 126-199
- By Alexander S. Kechris, California Institute of Technology, Donald A. Martin, UNIVERSITY OF CALIFORNIA LOS ANGELES, Robert M. Solovay, University of California, Berkeley
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On the theory of Π13 sets of reals, II
pp 200-219
- By Alexander S. Kechris, California Institute of Technology, Donald A. Martin, UNIVERSITY OF CALIFORNIA LOS ANGELES
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An inner models proof of the Kechris–Martin theorem
pp 220-242
- By Itay Neeman, UNIVERSITY OF CALIFORNIA LOS ANGELES
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A theorem of Woodin on mouse sets
pp 243-256
- By John R. Steel, University of California, Berkeley
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HOD as a core model
pp 257-346
- By John R. Steel, University of California, Berkeley, W. Hugh Woodin, University of California, Berkeley
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PART VI - RECURSION THEORY
pp 347-348
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Recursion theoretic papers. Introduction to Part VI
pp 349-354
- By Leo A. Harrington, University of California, Berkeley, Theodore A. Slaman, University of California, Berkeley
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On recursion in E and semi-Spector classes
pp 355-389
- By Phokion G. Kolaitis, UNIVERSITY OF CALIFORNIA, SANTA CRUZ
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On Spector classes
pp 390-423
- By Alexander S. Kechris, California Institute of Technology
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Trees and degrees
pp 424-457
- By Piergiorgio Odifreddi, UNIVERSITY OF CALIFORNIA LOS ANGELES
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Definable functions on degrees
pp 458-475
- By Theodore A. Slaman, University of California, Berkeley, John R. Steel, University of California, Berkeley
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Π12 monotone inductive definitions
pp 476-492
- By Donald A. Martin, UNIVERSITY OF CALIFORNIA LOS ANGELES
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Martin's conjecture, arithmetic equivalence, and countable Borel equivalence relations
pp 493-520
- By Andrew Marks, California Institute of Technology, Theodore A. Slaman, University of California, Berkeley, John R. Steel, University of California, Berkeley
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Bibliography
pp 521-535
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Ordinal Definability and Recursion Theory

The Cabal Seminar, Volume III

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-x

Original Numbering
pp xi-xvi

PART V - HOD AND ITS LOCAL VERSIONS
pp 1-2

Ordinal definability in models of determinacy. Introduction to Part V
pp 3-48

Partially playful universes
pp 49-85

Ordinal games and playful models
pp 86-114

Measurable cardinals in playful models
pp 115-125

Introduction to Q-theory
pp 126-199

On the theory of Π13 sets of reals, II
pp 200-219

An inner models proof of the Kechris–Martin theorem
pp 220-242

A theorem of Woodin on mouse sets
pp 243-256

HOD as a core model
pp 257-346

PART VI - RECURSION THEORY
pp 347-348

Recursion theoretic papers. Introduction to Part VI
pp 349-354

On recursion in E and semi-Spector classes
pp 355-389

On Spector classes
pp 390-423

Trees and degrees
pp 424-457

Definable functions on degrees
pp 458-475

Π12 monotone inductive definitions
pp 476-492

Martin's conjecture, arithmetic equivalence, and countable Borel equivalence relations
pp 493-520

Bibliography
pp 521-535

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Ordinal Definability and Recursion Theory

The Cabal Seminar, Volume III

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