Robert M. Solovay

Robert Martin Solovay (1938 – ) is a set theorist who spent many years as a professor at UC Berkeley. Among his most noted accomplishments are showing (relative to the existence of an inaccessible cardinal) that the statement "every set of real numbers is Lebesgue measurable" it is consistent with ZF, without the axiom of choice, and isolating the notion of 0^#. He proved that the existence of a real valued measurable cardinal is equiconsistent with the existence of a measurable cardinal. He also proved that if $lambda$ is a strong limit singular cardinal, greater than a strongly compact cardinal then $2^lambda=lambda^+$ holds. In another important result he proved that if $kappa$ is an uncountable regular cardinal, and $Ssubseteqkappa$ is a stationary set, then $S$ can be decomposed into the union of $kappa$ disjoint stationary sets.

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". Among his notable students are W. Hugh Woodin and Matthew Foreman.

Solovay has accomplishments outside of set theory as well; with Volker Strassen, he developed the Solovay-Strassen primality test, which is used to identify large natural numbers that are prime with high probability, and had important ramifications in the history of cryptography.

elected publications

*cite journal|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|year=1970|pages=1–56
*cite journal|author=Solovay, Robert M.|title=A nonconstructible "Δ¹₃" set of integers|journal=Transactions of the American Mathematical Society|volume=127|year=1967|pages=50–75|doi=10.2307/1994631
*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

ee also

*Provability logic

External links

*MathGenealogy|id=6522