Bernays, Paul (Isaak) (1888-1977)

English-born Swiss mathematician whose theory of sets is now widely believed to be the most useful arrangement, and a major contribution to the modern development of logic.

Bernays was born in London but grew up in Berlin and studied mathematics, philosophy, and theoretical physics at the universities of Berlin and Göttingen. He researched at Zürich, Switzerland, 1912-17, and then became German mathematician David Hilbert's assistant at Göttingen. In 1933, when the Nazis came to power in Germany, Bernays moved back to Zürich, where he eventually became a professor at the Technical High School.

Bernays became interested in axiomatic thoughts, and presented his principles of axiomatization most fully in lectures at the Princeton Institute for Advanced Study in 1935-36.

In Bernays' set theory there are two kinds of individuals: sets and classes. A set is a multitude forming a real mathematical object, whereas a class is a predicate to be regarded only with respect to its extension.