Matthew Foreman

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Matt Foreman

Matthew Dean Foreman (born March 21, 1957 in Los Alamos ) is an American mathematician who deals with the fundamentals of mathematics, axiomatic set theory and especially large cardinal numbers , and with descriptive set theory , with ergodic theory and dynamic systems.

Life

Foreman studied at the University of Colorado (Bachelor's degree in 1975) and received his doctorate in 1980 from the University of California, Berkeley , with Robert Solovay ( Large cardinals and model theoretical transfer properties ). As a post-doctoral student he was at the University of California, Los Angeles until 1982 , at the Hebrew University in 1983/84 and at Caltech from 1984 to 1986 . From 1986 he was Associate Professor of Mathematics (from 1990 also for Philosophy) at Ohio State University . He is a professor at the University of California, Irvine .

In 1988, with Menachem Magidor and Saharon Shelah, he proved 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 is false for any infinite cardinal number.

He dealt with descriptive set theory and its application in ergodic theory (working with Benjamin Weiss ).

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

In 1998 he was invited speaker at the International Congress of Mathematicians in Berlin ( Generic large cardinals. New axioms for arithmetic? ) And was selected as Gödel Lecturer in 2021.

He is a passionate sailor who has also won prizes (Ullman Trophy).

Fonts

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

Web links

Individual evidence

  1. ↑ Life data according to American Men and Women of Science , Thomson Gale 2004
  2. ^ Mathematics Genealogy Project
  3. ^ Foreman, Magidor, Shelah Martin's maximum, saturated ideals, and nonregular ultrafilters , Annals of Mathematics, Volume 127, 1988, Part 1 pp. 1-47, Part 2 pp. 521-545
  4. ^ Foreman, Woodin The generalized continuum hypothesis can fail everywhere , Annals of Mathematics, Volume 133, 1991, pp. 1-35
  5. ^ Ferenc Beleznay, Foreman The collection of distal flows is not Borel , American Journal of Mathematics, Volume 117, 1995, pp. 203-239. Beleznay is his PhD student
  6. ↑ Foreman, B. Weiss An anti-classification theorem for ergodic measure preserving transformations , J. European Math. Soc. (JEMS), Volume 6, 2004, pp. 277-292
  7. ^ Foreman, DJ Rudolph, B. Weiss The conjugacy problem in ergodic theory , Annals of Mathematics, Volume 173, 2011, pp. 1529–1586
  8. ↑ Foreman, R. Dougherty Banach-Tarski decompositions using sets with the property of Baire , J. Amer. Math. Soc., Vol. 7, 1994, pp. 75-124
  9. ^ Foreman, Wehrung The Hahn-Banach theorem implies the existence of a non-Lebesgue measurable set , Fundamenta Mathematicae, Volume 138, 1991, pp. 13-19
personal data
SURNAME Foreman, Matthew
ALTERNATIVE NAMES Foreman, Matthew Dean (full name)
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH March 21, 1957
PLACE OF BIRTH Los Alamos