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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. March 21 is the 80th day of the year in the Gregorian calendar (81st in leap years). ...
1957 (MCMLVII) was a common year starting on Tuesday of the Gregorian calendar. ...
Set theory is the mathematical theory of sets, which represent collections of abstract objects. ...
The University of California, Irvine is a public research university primarily situated in suburban Irvine, California; a significant portion of the campus falls into the neighboring community of Newport Beach. ...
In mathematics, descriptive set theory is the study of certain classes of well-behaved sets of real numbers, e. ...
In axiomatic set theory, forcing is a technique, invented by Paul Cohen, for proving consistency and independence results with respect to the Zermelo-Fraenkel axioms. ...
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. Doctor of Philosophy (Ph. ...
Sather tower (the Campanile) looking out over the San Francisco Bay and Mount Tamalpais. ...
Robert M. Solovay is a set theorist who spent many years as a professor at UC Berkeley. ...
This article is about the thesis in dialectics and academia. ...
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. W. Hugh Woodin is a set theorist at University of California, Berkeley. ...
The Banach–Tarski paradox: A ball can be decomposed and reassembled into two balls the same size as the original. ...
In topology and related branches of mathematics, a Baire space is a topological space in which, intuitively, there are enough points for certain limit processes. ...
Selected publications
- Foreman, Matthew (2006). "Has the continuum hypothesis been settled?". Logic Colloquium '03: 56–75, Assoc. Symbol. Logic, La Jolla, CA.
- 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.
- 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.
- 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.
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