Matthew Foreman

Matthew Dean Foreman ( born March 21, 1957 in Los Alamos ) is an American mathematician who is concerned with the foundations of mathematics, axiomatic set theory, and especially large cardinals, and with descriptive set theory, ergodic theory and dynamical systems with.

Foreman studied at the University of Colorado ( BA 1975) and in 1980 at the University of California, Berkeley, Robert Solovay doctorate (Large cardinals and model theoretic transfer properties ). As a post - graduate student, he was up in 1982 at the University of California, Los Angeles, 1983/84 at the Hebrew University, and 1984-1986 at Caltech. In 1986 he was Associate Professor of Mathematics ( since 1990 also for philosophy) at the Ohio State University. He is a professor at the University of California, Irvine.

He proved in 1988 with Menachem Magidor and Saharon Shelah the consistency of a generalization of Martin's Axiom ( Martin's maximum).

With W. Hugh Woodin, he showed the consistency of the statement that the Generalized Continuum Hypothesis for every infinite cardinal number is incorrect.

In 1994, he was with Randall Dougherty, that there are Banach Tarski decompositions of the unit sphere in which the quantities have the Baire property. So they solved a 1930 excepted by Edward Marczewski problem. With F. Wehrung he showed in 1991 that from the Hahn- Banach theorem implies the existence of non- Lebesgue measurable quantities ..

In 1998 he was invited speaker at the International Congress of Mathematicians in Berlin (Generic large cardinals. Axioms for arithmetic New? ).

He is a passionate sailor who won even prices ( Ullman Trophy ).

Writings

• Publisher with Akihiro Kanamori Handbook of Set Theory, 3 volumes, Springer Verlag 2010