Dieter Klaua

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Dieter Klaua (born July 22, 1930 in Chemnitz ; † April 14, 2014 in Karlsruhe ) was a German mathematician who became known primarily for his contributions to axiomatic set theory as the basis of mathematics .

Live and act

Dieter Klaua studied 1949-1954 mathematics at the University of Leipzig and in 1958 at the Humboldt University of Berlin with Karl Schröter with the work Computable Analysis Dr. phil. PhD . From 1959 he was a research assistant at the German Academy of Sciences in Berlin . In 1959 he completed his habilitation with the work, published in 1961, Construction of Whole, Rational and Real Ordinal Numbers and the Discontinuous Structure of Transfinite Real Number Spaces . In 1962 he was appointed lecturer at the Humboldt University in Berlin and in 1965 as a professor at the Karl Marx University in Leipzig . There he began with his students, including Siegfried Gottwald , to establish a multi-valued set theory as a foundation for a non-classical structure of mathematics.

Klaua ended his teaching activity in 1972 for health reasons, but he continued to work in basic mathematical research . From 1973 to 1975 he worked at the Mathematical Institute of the Medical Academy Berlin-Lichtenberg , in 1976 he retired , in 1977 he left the GDR and went to Karlsruhe .

Services

In his habilitation thesis, Dieter Klaua constructed ordered bodies in a uniform manner, which expand the field of real numbers and therefore have to contain both infinitesimal elements and infinitely large numbers ( generalized transfinite number spaces ). In 1965 he designed - parallel to and independently of Lotfi Zadeh - a generalized concept of sets with a graduated relationship of membership, the multivalued sets , using the multivalued logics according to Jan Łukasiewicz as the framework system. From around 1968 Dieter Klaua concentrated mainly on the three-valued case of his multivalent sets, which he called partial sets . With this he developed a set-theoretical foundation for interval arithmetic .

Fonts

  • Computable Analysis. Dissertation. Humboldt University Berlin. In: Journal for Mathematical Logic and Fundamentals of Mathematics. Volume 2, 1956, ISSN  0044-3050 , pp. 265-303.
  • Constructive Analysis. German Science Publishing House, Berlin 1961.
  • Construction of whole, rational and real ordinal numbers and the discontinuous structure of the transfinite real number spaces. Habilitation thesis. Humboldt University Berlin. Akademie-Verlag, Berlin 1961.
  • General set theory. Akademie-Verlag, Berlin 1964.
  • Elementary axioms of set theory. Akademie-Verlag, Berlin 1971, ISBN 3-528-06081-6 .
  • Basic concepts of axiomatic set theory. 2 parts. Akademie-Verlag, Berlin and Vieweg, Braunschweig 1973.
  • Cardinal and ordinal numbers. 2 parts. Akademie-Verlag, Berlin and Vieweg, Braunschweig 1974, ISBN 3-528-06125-1 and ISBN 3-528-06141-3 .
  • Quantity intervals. Institute for Applied Mathematics, Freiburg i. Br. 1978.
  • Set theory. de Gruyter, Berlin, New York 1979, ISBN 3-11-007726-4 .
  • Exact foundation of mathematics. 3 parts. Widmann, Karlsruhe 1987, 1988, ISBN 3-923314-04-3 , ISBN 3-923314-05-1 and ISBN 3-923314-06-X . New editions 1996.
  • Transfinite number systems based on the Cantor ordinal numbers. 2 parts. Widmann, Karlsruhe 1989, ISBN 3-923314-07-8 and ISBN 3-923314-08-6 . New editions 1996.
  • On a definition of surreal numbers by the rank relation. Widmann, Karlsruhe 1998, ISBN 3-923314-15-9 .

Web links

personal data
SURNAME Klaua, Dieter
BRIEF DESCRIPTION German mathematician
DATE OF BIRTH July 22, 1930
PLACE OF BIRTH Chemnitz
DATE OF DEATH April 14, 2014
Place of death Karlsruhe