Robert M. Solovay

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"Solovay" redirects here. For alleged internet "Spam King", see Robert Soloway. For people with similar names, see Soloway (disambiguation).

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 it is consistent with ZF, without the axiom of choice, that every set of real numbers is Lebesgue measurable, 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 $λ$ is a strong limit singular cardinal, greater than a strongly compact cardinal then $2 λ = λ +$ holds. In another important result he proved that if $κ$ is an uncountable regular cardinal, $S\subseteq\kappa$ is a stationary set, then $S$ can be decomposed into the union of $κ$ 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.

[edit] Selected publications

Solovay, Robert M. (1970). "A model of set-theory in which every set of reals is Lebesgue measurable". Annals of Mathematics. Second Series 92: 1–56.
Solovay, Robert M. (1967). "A nonconstructible Δ¹₃ set of integers". Transactions of the American Mathematical Society 127: 50–75.
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.