Skolem, Thoralf Albert

Born May 23, 1887, in Sandsvær; died Mar. 23, 1963, in Oslo. Norwegian mathematician, logician, and philosopher.

Skolem graduated from the University of Oslo in 1913 and was appointed a professor there in 1938. He became a member of the Norwegian Academy of Science in 1938. Skolem’s works deal with the theory of numbers and various problems of logic and the philosophy of mathematics. His best-known result is the Skolem-Löwenheim theorem, according to which any axiomatic theory that has an infinite model also has a denumerable model. From this result follows Skolem’s paradox—that is, the relativity of such concepts as the denumerability, nondenumer-ability, and cardinal number of a set. The Skolem-Löwenheim theorem also implies the possibility of constructing nonstandard models of axiomatic theories (seeMODEL THEORY). Skolem’s results and ideas are used in research on computerized search for logical proofs.