Paul Bernays
1888-1977
Swiss mathematician who contributed to mathematical logic and set theory, particularly in the framework of David Hilbert's systematic analysis of proofs. In his early work on propositional logic (the logic of sentential connectives such as "and," "or," "if-then," and negation), he showed that the system of Bertrand Russell and A.
N. Whitehead was complete, in the sense that all valid formulas are provable. Later Bernays developed an axiomatization of set theory in first order logic with three fundamental notions—membership, set, and class—in order to avoid the contradictions of earlier systems.
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