Ordinal Definability and Recursion Theory: Volume 3

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is the third in a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics and discussion of research developments since the publication of the original volumes.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.Preface Alexander S. Kechris, Benedikt Lowe 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 models 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 VI Leo A. Harrington and Theodore A. Slaman; On recursion in E and semi-Spector classes 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 relations Andrew Marks, Theodore A. Slaman and John R. Steel; Bibliography.