Cabal (set theory)

The Cabal was, or perhaps is, a set of set theorists in Southern California, particularly at UCLA and Caltech, but 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.

Some of the philosophical views of the Cabal seminar were described in {{harvnb|Maddy|1988a}} and {{harvnb|Maddy|1988b}}.

Publications

{{cite book |author=Kechris, A. S. |title=Cabal Seminar 76-77: Proceedings of the Caltech-UCLA Logic Seminar 1976–77 |publisher=Springer |year=1978 |isbn=0-387-09086-X |display-authors=etal |url-access=registration |url=https://archive.org/details/cabalseminar76770689caba}}
{{cite book |editor=Kechris, A. S. |title=Cabal Seminar 79-81: Proceedings of the Caltech-UCLA Logic Seminar 1979–81 |series=Lecture Notes in Mathematics |year=1983 |publisher=Springer |isbn=0-387-12688-0}}
{{cite book|author1=Martin, D. A. |author2=A. S. Kechris |author3=J. R. Steel |title=Cabal Seminar 81–85: Proceedings of the Caltech UCLA Logic Seminar |series=Lecture Notes in Mathematics |volume=1333 |year=1988 |publisher=Springer |isbn=0-387-50020-0}}
{{cite book |author1=Alexander S. Kechris |author2=Benedikt Löwe |author2-link= Benedikt Löwe |author3=John R. Steel |title=Games, Scales, and Suslin Cardinals: The Cabal Seminar Volume I |series=Lecture Notes in Logic |year=2008 |publisher=Cambridge University Press |isbn=9780521899512}}

{{cite journal|last=Maddy|first=Penelope|author-link=Penelope Maddy|title=Believing the Axioms I|journal=The Journal of Symbolic Logic|year=1988a|volume=53|number=2|pages=481–511|url=http://www.cs.umd.edu/~gasarch/BLOGPAPERS/belaxioms1.pdf|doi=10.1017/s0022481200028425}}
{{cite journal|last=Maddy|first=Penelope|author-link=Penelope Maddy|title=Believing the Axioms II|journal=The Journal of Symbolic Logic|year=1988b|volume=53|number=3|pages=736–764|url=http://www.cs.umd.edu/~gasarch/BLOGPAPERS/belaxioms2.pdf|doi=10.2307/2274569|jstor=2274569 }}