The Cabal was, or perhaps is, a grouping 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

Donald A. Martin

Donald A. Martin is a set theorist and philosopher of mathematics at UCLA, where he is a member of the faculty of mathematics and philosophy....

, Yiannis N. Moschovakis

Yiannis N. Moschovakis

Yiannis Nicholas Moschovakis is a set theorist, descriptive set theorist, and recursion theorist, at UCLA. For many years he has split his time between UCLA and University of Athens . His book Descriptive Set Theory is the primary reference for the subject...

, John R. Steel

John R. Steel

John Robert Steel is a set theorist at University of California, Berkeley . He has made many contributions to the theory of inner models and determinacy. With Donald A. Martin, he proved projective determinacy, assuming the existence of sufficient large cardinals. He earned his Ph.D...

, and Alexander S. Kechris

Alexander S. Kechris

Alexander Sotirios Kechris is a descriptive set theorist at Caltech. He has made major contributions to the theory of Borel equivalence relations....

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

Robert M. Solovay

Robert Martin Solovay is an American mathematician specializing in set theory.Solovay earned his Ph.D. from the University of Chicago in 1964 under the direction of Saunders Mac Lane, with a dissertation on A Functorial Form of the Differentiable Riemann–Roch theorem...

, W. Hugh Woodin

W. Hugh Woodin

William Hugh Woodin is an American mathematician and set theorist at University of California, Berkeley. He has made many notable contributions to the theory of inner models and determinacy. A type of large cardinal, the Woodin cardinal, bears his name.-Biography:Born in Tucson, Arizona, Woodin...

, Matthew Foreman

Matthew Foreman

Matthew Dean Foreman is a set theorist at University of California, Irvine. He has made contributions in widely varying areas of set theory, including descriptive set theory, forcing, and infinitary combinatorics....

, and Steve Jackson

Steve Jackson (mathematician)

Steve Jackson is a set theorist at University of North Texas. Much of his most notable work has involved the descriptive set-theoretic consequences of the axiom of determinacy...

.

The work of the group is characterized by free use of large cardinal axioms, and research into the descriptive set theoretic

Descriptive set theory

In mathematical logic, descriptive set theory is the study of certain classes of "well-behaved" subsets of the real line and other Polish spaces...

 behavior of sets of reals

Real number

In mathematics, a real number is a value that represents a quantity along a continuum, such as -5 , 4/3 , 8.6 , √2 and π...

if such assumptions hold.