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 $σ$ -complete, $\aleph_1$ -dense ideal on $\aleph_2$ .

With Akihiro Kanamori he is the editor of the monumental Handbook of Set Theory (to appear in 2008).

He is known for his excellent sense of humor. He is also an avid sailor.

[edit] Selected publications

Foreman, Matthew (2006). "Has the continuum hypothesis been settled?". Logic Colloquium '03: 56–75, Assoc. Symbol. Logic, La Jolla, CA. link
Foreman, Matthew and Menachem Magidor (1995). "Large cardinals and definable counterexamples to the continuum hypothesis". Annals of Pure and Applied Logic 76 (1): 47–97. doi:10.1016/0168-0072(94)00031-W.
Dougherty, Randall and Matthew Foreman (1994). "Banach-Tarski decompositions using sets with the property of Baire". Journal of the American Mathematical Society 7 (1): 75–124. doi:10.2307/2152721.
Foreman, Matthew and Friedrich Wehrung (1991). "The Hahn-Banach theorem implies the existence of a non-Lebesgue measurable set". Fundamenta Mathematicae 138 (1): 13–19.
Foreman, Matthew and W. Hugh Woodin (1991). "The generalized continuum hypothesis can fail everywhere". Annals of Mathematics (2) 133 (1): 1–35. doi:10.2307/2944324.