## Ordinal Definability and Recursion Theory

Alexander S. Kechris, Benedikt Lowe, John R. Steel (Editors)

Year: 2016

ISBN-13: 9781107033405

552 pages. Hardcover.

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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is the third in a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics and discussion of research developments since the publication of the original volumes.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.

• Includes updated/revised material from the original Cabal Seminars volume • New, unpublished survey articles put the historical papers into context • Now includes uniform and modern notation to make the book more accessible to the reader

### Table of Contents

- Preface Alexander S. Kechris, Benedikt Löwe and John R. Steel
- Original numbering

**Part V. HOD and its Local Versions:**

- Ordinal definability in models of determinacy, Introduction to Part V, John R. Steel
- Partially playful universes, Howard S. Becker
- Ordinal games and playful models, Yiannis N. Moschovakis
- Measurable cardinals in playful model,s Howard S. Becker and Yiannis N. Moschovakis
- Introduction to Q-theory, Alexander S. Kechris, Donald A. Martin and Robert M. Solovay
- On the theory of ∏1/3 sets of reals, II, Alexander S. Kechris and Donald A. Martin
- An inner models proof of the Kechris–Martin theorem, Itay Neeman
- A theorem of Woodin on mouse sets, John R. Steel
- HOD as a core model, John R. Steel and W. Hugh Woodin
- Part VI. Recursion Theory: Recursion theoretic papers – Introduction to Part V,I Leo A. Harrington and Theodore A. Slaman
- On recursion in E and semi-Spector classe,s Phokion G. Kolaitis
- On Spector classes, Alexander S. Kechris
- Trees and degrees, Piergiorgio Odifreddi
- Definable functions on degrees, Theodore A. Slaman and John R. Steel
- ∏1/2 monotone inductive definitions, Donald A. Martin
- Martin’s conjecture, arithmetic equivalence, and countable Borel equivalence relation,s Andrew Marks, Theodore A. Slaman and John R. Steel
- Bibliography.