Skolem, Thoralf Albert

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.

WORKS

Selected Works in Logic. Boston, 1970. [23–1531–]