MATTHEW FOREMAN

'Matthew Foreman' (born March 21, 1957) 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.
Foreman earned his Ph.D. in 1980 at University of California, Berkeley under the direction of Robert M. Solovay, with a dissertation on ''Large Cardinals and Model Theoretic Transfer Properties''.
With W. Hugh Woodin he proved consistent that the Generalized Continuum Hypothesis fails everywhere. With Randall Dougherty he showed that the Banach-Tarski decomposition is possible with pieces with the Baire property. With Menachem Magidor and Saharon Shelah they formulated and proved the consistency of Martin's Maximum, a provably maximal form of Martin's axiom. He further proved consistent (from the consistency of a huge cardinal) that there exists a $sigma$-complete, -dense ideal on .
He is also known for his sense of humor.

Contents

Selected publications

External links

Selected publications

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★ Large cardinals and definable counterexamples to the continuum hypothesis, Foreman, Matthew and Menachem Magidor, , , Annals of Pure and Applied Logic, 1995

★ Banach-Tarski decompositions using sets with the property of Baire, Dougherty, Randall and Matthew Foreman, , , Journal of the American Mathematical Society, 1994

★ The Hahn-Banach theorem implies the existence of a non-Lebesgue measurable set, Foreman, Matthew and Friedrich Wehrung, , , Fundamenta Mathematicae, 1991

★ The generalized continuum hypothesis can fail everywhere, Foreman, Matthew and W. Hugh Woodin, , , Annals of Mathematics (2), 1991

External links

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