# Paul Bernays

Paul Bernays ( born October 17, 1888 in London, † September 18, 1977 in Zurich ) was a mathematician and logician.

## Life

He came from a German - Jewish family of scholars and was a citizen of the city of Zurich. From London to Paris Paul Bernays came up with seven years in Berlin, where he 1907 on the Köllner school passed his A -levels and decided in the conflict between his strong musical inclination and his interest in mathematics to the study of the latter: first in Berlin at the TH, then the university and in 1909 in Göttingen. In addition to his studies, graduating in 1912 with a dissertation on Edmund Landau, he engaged extensively in the circle of the philosopher Leonard Nelson, the New Fries'schen school, which he - as a member, founded by Nelson 1912/13, Jakob Friedrich- Fries society and after the First world War, launched the Society of Friends of the Philosophical- Political Academy - remained a lifelong.

From 1912 to 1917 he was a lecturer in Zurich, returned in 1919 to Göttingen, where he became associate professor in 1922. As a Jew, he lost his place in Göttingen in 1933 and then returned to Switzerland.

From 1945 to 1958 he was professor at the ETH Zurich. In 1947 he founded together with Gaston Bachelard and Ferdinand Gonseth the philosophical journal Dialectica.

## Performance

Bernays built the proof theory of David Hilbert from further, with whom he released the for the most part written by him alone work on the foundations of mathematics. Then he put on years before work on axiomatic set theory. His set theory with classes formed an essential basis for later Neumann - Bernays - Gödel set theory.

## Works

- David Hilbert and Paul Bernays: Fundamentals of Mathematics I -II, Berlin 1934/1939
- Paul Bernays: A System of Axiomatic Set Theory I-VII, in: Journal of Symbolic Logic, Part I in Volume 2 (1937 ), pp. 65-77; In Part II, Volume 6 (1941 ), pp. 1-17, Part III in Volume 7 (1942 ), pp. 65ff, Part IV of Volume 7 (1942 ), pp. 133ff, Part V in Volume 8 (1943 ), S. 89ff, Part VI in Volume 13 (1948 ), pp. 65ff, Part VII in Volume 19 (1954 ), pp. 81ff. Total Edition: Sets and classes, on the work of Paul Bernays, editor Gert H. Müller, Amsterdam, New York, Oxford, 1976, p.1 -119.
- Paul Bernays: Axiomatic Set Theory, Amsterdam 1958
- Essays on the Philosophy of Mathematics. , Darmstadt 1976
- Leonard Nelson: Collected Writings. Edited by Paul Bernays, Willi Eichler, Arnold Gysin, Gustav Heckmann, Grete Henry -Hermann, Fritz von Hippel, Stephan Körner, Gerhard Weisser, Werner Kroebel. Felix Meiner Verlag, Hamburg 1970-1977