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| {{Redirect6|Solovay|alleged internet "Spam King"|Robert Soloway|people with similar names|Soloway (disambiguation)}}
| | Hi there. Allow me begin by introducing the writer, her title is Sophia Boon but she never really liked that title. What I adore doing is football but I don't have the time lately. Ohio is exactly where her house is. Credit authorising is how she tends to make a residing.<br><br>Feel free to visit my web site - best psychic ([http://isaworld.pe.kr/?document_srl=392088 isaworld.pe.kr]) |
| {{no footnotes|date=February 2013}}
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| {{Infobox scientist
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| | name = Robert M. Solovay
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| | image = Robert Solovay.jpeg
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| | image_size = 200px
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| | caption = Robert Solovay in 1972 (photo by George Bergman)
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| | birth_date = {{Birth date and age|1938|12|15|mf=y}}
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| | birth_place = [[Brooklyn, New York]], U.S.
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| | death_date =
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| | death_place =
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| | nationality = [[United States|American]]
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| | fields = [[Mathematics]]
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| | workplaces = [[University of California, Berkeley]]
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| | alma_mater = [[University of Chicago]]
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| | doctoral_advisor = [[Saunders Mac Lane]]
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| | doctoral_students = [[Matthew Foreman]]<br>[[Kenneth McAloon]]<br>[[Judith Roitman]]<br>[[W. Hugh Woodin]]
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| | known_for =
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| | awards =
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| }}
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| '''Robert Martin Solovay''' (born December 15, 1938) is an [[United States|American]] [[mathematician]] specializing in [[set theory]].
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| Solovay earned his [[Ph.D.]] from the [[University of Chicago]] in 1964 under the direction of [[Saunders Mac Lane]], with a dissertation on ''A Functorial Form of the Differentiable [[Riemann–Roch theorem]]''. Solovay has spent his career at the [[University of California]] at Berkeley, where his notable Ph.D. students include [[W. Hugh Woodin]] and [[Matthew Foreman]].
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| Solovay's noted accomplishments include:
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| * [[Solovay's theorem]] showing that, if one assumes the existence of an [[inaccessible cardinal]], then the statement "every [[Set (mathematics)|set]] of [[real number]]s is [[Lebesgue measurable]]" is consistent with [[Zermelo–Fraenkel set theory|ZF]] without the [[axiom of choice]];
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| * Isolating the notion of [[zero sharp|0<sup>#</sup>]];
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| * Proving that the existence of a [[measurable cardinal#Real-valued measurable|real valued measurable cardinal]] is [[equiconsistency|equiconsistent]] with the existence of a measurable cardinal;
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| * Proving that if <math>\lambda</math> is a strong limit [[singular cardinal]], greater than a [[strongly compact cardinal]] then <math>2^\lambda=\lambda^+</math> holds;
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| * Proving that if <math>\kappa</math> is an uncountable regular cardinal, and <math>S\subseteq\kappa</math> is a [[stationary set]], then <math>S</math> can be decomposed into the union of <math>\kappa</math> disjoint stationary sets;
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| * Outside of set theory, developing (with [[Volker Strassen]]) the [[Solovay–Strassen primality test]], used to identify large [[natural number]]s that are [[prime number|prime]] with high [[probability]]. This method has had important ramifications for [[cryptography]].
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| * Proving that GL (the [[normal modal logic]] which has the instances of the schema <math>\Box(\Box A\to A)\to\Box A</math> as additional axioms) completely axiomatizes the logic of the provability predicate of [[Peano Arithmetic]].
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| == Selected publications ==
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| * {{cite journal|doi=10.2307/1970696|author=Solovay, Robert M.|title=A model of set-theory in which every set of reals is Lebesgue measurable|journal=Annals of Mathematics. Second Series|volume=92|issue=1|year=1970|pages=1–56}}
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| * {{cite journal|author=Solovay, Robert M.|title=A nonconstructible ''Δ<sup>1</sup><sub>3</sub>'' set of integers|journal=Transactions of the American Mathematical Society|volume=127|year=1967|pages=50–75|doi=10.2307/1994631|issue=1|publisher=American Mathematical Society|jstor=1994631}}
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| * {{cite journal|author=Solovay, Robert M. and Volker Strassen|journal=SIAM Journal on Computing|title=A fast Monte-Carlo test for primality|volume=6|year=1977|issue=1|pages=84–85|doi=10.1137/0206006}}
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| == See also ==
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| * [[Provability logic]]
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| == External links ==
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| * {{MathGenealogy|id=6522}}
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| * {{DBLP|id=Solovay:Robert}}
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| {{Kanellakis Award laureates}}
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| {{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
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| | NAME = Solovay, Robert M.
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| | ALTERNATIVE NAMES =
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| | SHORT DESCRIPTION = American mathematician
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| | DATE OF BIRTH = December 15, 1938
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| | PLACE OF BIRTH = [[Brooklyn, New York]], U.S.
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| | DATE OF DEATH =
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| | PLACE OF DEATH =
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| }}
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| {{DEFAULTSORT:Solovay, Robert M.}}
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| [[Category:American logicians]]
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| [[Category:Members of the United States National Academy of Sciences]]
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| [[Category:20th-century mathematicians]]
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| [[Category:Set theorists]]
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| [[Category:1938 births]]
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| [[Category:Living people]]
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| {{US-mathematician-stub}}
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