Robert M. Solovay
Robert Solovay in 1993 (photo by George Bergman)
Born	(1938-12-15)December 15, 1938 (age 86) Brooklyn, New York, U.S.
Nationality	American
Alma mater	University of Chicago
Known for	Solovay model Solovay–Strassen primality test Zero sharp Martin's axiom Solovay–Kitaev theorem
Awards	Paris Kanellakis Award(2003)
Scientific career
Fields	Mathematics
Institutions	University of California, Berkeley
Doctoral advisor	Saunders Mac Lane
Doctoral students	Matthew Foreman Judith Roitman Betül Tanbay W. Hugh Woodin

Robert Martin Solovay (born December 15, 1938) is an Americanmathematician working inset theory.

Solovay earned hisPh.D. from theUniversity of Chicago in 1964 under the direction ofSaunders Mac Lane, with a dissertation onA Functorial Form of the DifferentiableRiemann–Roch theorem.^[1] Solovay has spent his career at theUniversity of California at Berkeley, where his Ph.D. students includeW. Hugh Woodin andMatthew Foreman.^[2]

Solovay's theorems include:

• Solovay's theorem showing that, if one assumes the existence of aninaccessible cardinal, then the statement "everyset ofreal numbers isLebesgue measurable" is consistent withZermelo–Fraenkel set theory without theaxiom of choice;
• Isolating the notion of0^#;
• Proving that the existence of areal-valued measurable cardinal isequiconsistent with the existence of a measurable cardinal;
• Proving that if${\displaystyle \lambda }$ is a strong limitsingular cardinal, greater than astrongly compact cardinal then${\displaystyle 2^{\lambda }={\lambda }^{+}}$ holds;
• Proving that if${\displaystyle \kappa }$ is an uncountable regular cardinal, and${\displaystyle S\subseteq \kappa }$ is astationary set, then${\displaystyle S}$ can be decomposed into the union of${\displaystyle \kappa }$ disjoint stationary sets;
• WithStanley Tennenbaum, developing the method of iterated forcing and showing the consistency ofSuslin's hypothesis;
• WithDonald A. Martin, showed the consistency ofMartin's axiom with arbitrarily largecardinality of the continuum;
• Outside of set theory, developing (withVolker Strassen) theSolovay–Strassen primality test, used to identify largenatural numbers that areprime with highprobability. This method has had implications forcryptography;
• Regarding theP versus NP problem, he proved with T. P. Baker and J. Gill that relativizing arguments cannot prove${\displaystyle \mathrm{P}\ne \mathrm{N}\mathrm{P}}$.^[3]
• Proving that GL (thenormal modal logic which has the instances of the schema${\displaystyle ◻(◻A\to A)\to ◻A}$ as additional axioms) completely axiomatizes the logic of the provability predicate ofPeano arithmetic;
• WithAlexei Kitaev, proving that a finite set ofquantum gates can efficiently approximate an arbitraryunitary operator on onequbit in what is now known asSolovay–Kitaev theorem.

• Solovay, Robert M. (1970). "A model of set-theory in which every set of reals is Lebesgue measurable".Annals of Mathematics. Second Series.92 (1):1–56.doi:10.2307/1970696.JSTOR 1970696.
• Solovay, Robert M. (1967). "A nonconstructibleΔ¹₃ set of integers".Transactions of the American Mathematical Society.127 (1). American Mathematical Society:50–75.doi:10.2307/1994631.JSTOR 1994631.
• Solovay, Robert M. and Volker Strassen (1977). "A fast Monte-Carlo test for primality".SIAM Journal on Computing.6 (1):84–85.doi:10.1137/0206006.

• Provability logic

• Robert M. Solovay at theMathematics Genealogy Project
• Robert Solovay atDBLP Bibliography Server

• American logicians
• Members of the United States National Academy of Sciences
• 20th-century American mathematicians
• Set theorists
• 1938 births
• Living people

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