The proceedings of the Los Angeles Caltech-UCLA 'Cabal Seminar' were originally published in the 1970s and 1980s. Wadge Degrees and Projective Ordinals is the second of a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics and discussion of research developments since the publication of the original volumes.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 'Wadge Degrees and Pointclasses' (Part III) and 'Projective Ordinals' (Part IV), 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.
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 Loewe is Universitair Docent in Logic in the Institute for Logic, Language and Computation at the Universiteit van Amsterdam and Professor of Mathematics at the Universitat Hamburg. He is the vice-president of the Deutsche Vereinigung fur Mathematische Logik und fur Grundlagenforschung der Exakten Wissenschaften (DVMLG) and a Managing Editor of the journal Mathematical Logic Quarterly. 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.
Preface; Original numbering; Part III. Wadge Degrees and Pointclasses: Introduction to Part III Alessandro Andretta and Alain Louveau; 1. Wadge degrees and descriptive set theory Robert Van Wesep; 2. A note on Wadge degrees Alexander S. Kechris; 3. Some results in the Wadge hierarchy of Borel sets Alain Louveau; 4. The strength of Borel Wadge Determinacy Alain Louveau and Jean Saint-Raymond; 5. Closure properties of pointclasses John R. Steel; 6. The axiom of determinacy and the prewellordering property Alexander S. Kechris, Robert M. Solovay and John R. Steel; 7. Pointclasses and wellordered unions Steve Jackson and Donald A. Martin; 8. More closure properties of pointclasses Howard S. Becker; 9. More measures from AD John R. Steel; 10. The Borel degrees William W. Wadge; Part IV. Projective Ordinals: Introduction to Part IV Steve Jackson; 11. Homogeneous trees and projective scales Alexander S. Kechris; 12. AD and projective ordinals Alexander S. Kechris; 13. A 1/3 coding of the subsets of Robert M. Solovay; 14. AD and projective ordinals Steve Jackson; 15. Projective sets and cardinal numbers: some questions related to the continuum problem Donald A. Martin; 16. Regular cardinals without the weak partition property Steve Jackson; Bibliography.