Matthew Foreman
| Matthew Dean Foreman | |
|---|---|
 |
|
| Born |
March 21, 1957 Los Alamos, New Mexico, U.S. |
| Nationality | American |
| Fields | Mathematics |
| Institutions |
University of California, Irvine Ohio State University |
| Alma mater | University of California, Berkeley |
| Doctoral advisor | Robert M. Solovay |
Matthew Dean Foreman (born March 21, 1957) is an American mathematician at University of California, Irvine. He has made notable contributions in set theory and in ergodic theory.
Born in Los Alamos, New Mexico, Foreman earned his Ph.D. from the University of California, Berkeley in 1980 under Robert M. Solovay. His dissertation title was Large Cardinals and Strong Model Theoretic Transfer Properties.
In addition to his mathematical work, Foreman is an avid sailor. He and his family sailed their sailboat Veritas (a C&C 44 C&C Yachts) from North America to Europe in 2000. From 2000–2008 they sailed Veritas to the Arctic, the Shetland Islands, Scotland, Ireland, England, France, Spain, North Africa and Italy. Notable high points were Fastnet Rock, Irish and Celtic seas and many passages including the Maelstrom, Stad, Pentland Firth, Loch Ness, the Corryveckan and the Irish Sea. Further south they sailed through the Chenal du Four and Raz de Sein, across the Bay of Biscay and around Cape Finisterre. After entering Gibraltar, Foreman and his family circumnavigated the Western Mediterranean with notable stops in Barcelona, Morocco, Tunisia, Sicily, Naples, Sardinia and Corsica. In 2009, Foreman and his son and guest crew circumnavigated Newfoundland. Foreman has been recognized for his sailing by twice winning the Ullman Trophy.
Foreman began his career in set theory. His early work with Hugh Woodin included showing that it is consistent that the Generalized Continuum Hypothesis (GCH) (see Continuum Hypothesis) fails at every infinite cardinal. In joint work with Magidor and Shelah he formulated Martin's maximum, a provably maximal form of Martin's axiom and showed its consistency. Foreman's later work in set theory was primarily concerned with developing the consequences of generic large cardinal axioms. He also worked on classical "Hungarian" partition relations, mostly with András Hajnal.
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