Cabal (set theory)

The Cabal was, or perhaps is, a grouping of set theorists in Southern California, particularly at UCLA and Caltech, perhaps also at UC Irvine. Organization and procedures range from informal to nonexistent, so it is difficult to say whether it still exists or exactly who has been a member, but it has included such notable figures as Donald A. Martin, Yiannis N. Moschovakis, John R. Steel, and Alexander S. Kechris. Others who have published in the proceedings of the Cabal seminar include Robert M. Solovay, W. Hugh Woodin, Matthew Foreman, and Steve Jackson.

The work of the group is characterized by free use of large cardinal axioms, and research into the descriptive set theoretic behavior of sets of reals if such assumptions hold.

Publications

*cite book|author=Kechris, A. S. et al|title=Cabal Seminar 76-77: Proceedings. Caltech-UCLA Logic Seminar 1976-77|publisher=Springer|year=1978|id=ISBN 0-387-09086-X
*cite book|author=Kechris, A. S. (editor)|title=Cabal Seminar 79-81: Proc Caltech-UCLA Logic Seminar 1979-81 (Lecture Notes in Mathematics)|year=1983|publisher=Springer|id=ISBN 0-387-12688-0

*cite book|author=Martin, D. A., A. S. Kechris, J. R. Steel|title=Cabal Seminar 81-85: Proceedings Caltech UCLA Logic Seminar (Lecture Notes in Mathematics, No 1333)|year=1988|publisher=Springer|id=ISBN 0-387-50020-0

*cite book|author=Alexander S. Kechris, Benedikt Löwe, John R. Steel|title=Games, Scales, and Suslin cardinals: The Cabal Seminar Volume I: Lecture Notes in Logic|year=2008|publisher=CUP|id=ISBN-13: 9780521899512