 Bernays, Paul Isaak

▪ Swiss logician and mathematicianborn October 17, 1888, London, Englanddied September 18, 1977, Zürich, SwitzerlandSwiss mathematician whose work in proof theory and axiomatic set theory (set theory) helped create the new discipline of mathematical logic (logic).After obtaining his doctorate from the University of Göttingen (Göttingen, University of) in Germany under Edmund Landau in 1912, Bernays taught for five years at the University of Zürich before returning to Göttingen. There he collaborated closely with the prominent mathematician David Hilbert (Hilbert, David), who in the twilight of his career sought to overcome the challenges to classical mathematics posed by L.E.J. Brouwer (Brouwer, Luitzen Egbertus Jan)'s intuitionism. Bernays's own philosophical views remained in the background during the “foundations crisis” of the 1920s (see mathematics, foundations of: The quest for rigour (mathematics, foundations of)). Nevertheless, he served as a strong pillar of support for Hilbert's program to formalize mathematics (see formalism). Taking Hilbert's name as coauthor, he wrote the classic study Grundlagen der Mathematik, 2 vol. (1934–39; reissued 1968–70; “Foundations of Mathematics”). In 1956 Bernays also revised Hilbert's Grundlagen der Geometrie (1899; The Foundations of Geometry), which went through several editions.After the Nazi takeover in 1933, Bernays was compelled to give up his post and moved to Switzerland. In Zürich he delved into the realm of set theory, trying to streamline the ZermeloFraenkel system of axioms (see logic, history of: 20thcentury set theory (logic, history of)). This work appeared in a series of articles under the title “A System of Axiomatic Set Theory” (1937–54), from which the principal theses were published as Axiomatic Set Theory (1958). In it Bernays simplified and refined the work of John von Neumann (von Neumann, John) on logic and set theory; these modifications were further developed by the logician Kurt Gödel (Gödel, Kurt).
* * *
Universalium. 2010.
Look at other dictionaries:
Bernays — ist der Familienname folgender Personen: Chacham Isaak Bernays, (1792–1849) Oberrabbiner der Deutsch Israelitischen Gemeinde in Hamburg, Vorreiter der modernen Orthodoxie Edward Bernays (1891–1995), Public Relations Forscher, Urenkel von Isaak… … Deutsch Wikipedia
Jacob Bernays — (* 11. September 1824 in Hamburg; † 26. Mai 1881 in Bonn) war ein deutscher Klassischer Philologe und Bruder von Michael Bernays. Inhaltsverzeichnis 1 Leben 2 Werk 3 Schriften … Deutsch Wikipedia
logic, history of — Introduction the history of the discipline from its origins among the ancient Greeks to the present time. Origins of logic in the West Precursors of ancient logic There was a medieval tradition according to which the Greek philosopher … Universalium
set theory — the branch of mathematics that deals with relations between sets. [1940 45] * * * Branch of mathematics that deals with the properties of sets. It is most valuable as applied to other areas of mathematics, which borrow from and adapt its… … Universalium
Mac Lane, Saunders — ▪ 2006 American mathematician (b. Aug. 4, 1909, Taftville, Conn. d. April 14, 2005, San Francisco, Calif.), made significant contributions to modern algebra and topology and, with Samuel Eilenberg, was a cofounder of category theory, which… … Universalium
metalogic — /met euh loj ik/, n. the logical analysis of the fundamental concepts of logic. [1835 45; META + LOGIC] * * * Study of the syntax and the semantics of formal languages and formal systems. It is related to, but does not include, the formal… … Universalium
Liste der Biografien/Bern — Biografien: A B C D E F G H I J K L M N O P Q … Deutsch Wikipedia
List of German Jews — The Jewish presence in Germany is older than Christianity; the first Jewish population came with the Romans to the city Cologne. A Golden Age in the first millennium saw the emergence of the Ashkenazi Jews, while the persecution and expulsion… … Wikipedia
Liste Hundertjähriger — Diese Liste enthält Persönlichkeiten, die ihr hundertstes Lebensjahr vollenden konnten. Nicht enthalten sind Altersrekordhalter, deren Bekanntheit ausschließlich auf ihrem hohen Alter beruht. Hundertjährige Persönlichkeiten von heute Personen,… … Deutsch Wikipedia
Liste der Hundertjährigen — Diese Liste enthält Persönlichkeiten, die ihr hundertstes Lebensjahr vollenden konnten. Nicht enthalten sind Altersrekordhalter, deren Bekanntheit ausschließlich auf ihrem hohen Alter beruht. Hundertjährige Persönlichkeiten von heute Personen,… … Deutsch Wikipedia