The Cabal was, or perhaps is, a set of set theorists in

Southern California Southern California (commonly shortened to SoCal) is a geographic and cultural region that generally comprises the southern portion of the U.S. state of California. It includes the Los Angeles metropolitan area, the second most populous urban ...

, particularly at

UCLA The University of California, Los Angeles (UCLA) is a public land-grant research university in Los Angeles, California. UCLA's academic roots were established in 1881 as a teachers college then known as the southern branch of the California ...

and

Caltech The California Institute of Technology (branded as Caltech or CIT)The university itself only spells its short form as "Caltech"; the institution considers other spellings such a"Cal Tech" and "CalTech" incorrect. The institute is also occasional ...

, but also at

UC Irvine UC may refer to: Arts and entertainment * '' University Challenge'', a popular British quiz programme airing on BBC Two ** ''University Challenge (New Zealand)'', the New Zealand version of the British programme * Universal Century, one of the t ...

. 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 Donald Anthony Martin (born December 24, 1940), also known as Tony Martin, is an American set theorist and philosopher of mathematics at UCLA, where he is an emeritus professor of mathematics and philosophy. Education and career Martin receiv ...

, Yiannis N. Moschovakis, John R. Steel, and

Alexander S. Kechris Alexander Sotirios Kechris ( el, Αλέξανδρος Σωτήριος Κεχρής; born March 23, 1946) is a set theorist and logician at the California Institute of Technology. Contributions Kechris has made contributions to the theory of B ...

. Others who have published in the proceedings of the Cabal seminar include

Robert M. Solovay Robert Martin Solovay (born December 15, 1938) is an American mathematician specializing in set theory. Biography Solovay earned his Ph.D. from the University of Chicago in 1964 under the direction of Saunders Mac Lane, with a dissertation on '' ...

W. Hugh Woodin William Hugh Woodin (born April 23, 1955) is an American mathematician and set theorist at Harvard University. He has made many notable contributions to the theory of inner models and determinacy. A type of large cardinals, the Woodin cardinals, ...

Matthew Foreman Matthew Dean Foreman is an American mathematician at University of California, Irvine. He has made notable contributions in set theory and in ergodic theory. Biography Born in Los Alamos, New Mexico, Foreman earned his Ph.D. from the Univers ...

, and Steve Jackson. The work of the group is characterized by free use of

large cardinal In the mathematical field of set theory, a large cardinal property is a certain kind of property of transfinite cardinal numbers. Cardinals with such properties are, as the name suggests, generally very "large" (for example, bigger than the least ...

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 and .

Publications

* * * *

References

* * Descriptive set theory Set theory {{settheory-stub