W. Hugh Woodin

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Hugh Woodin 1994

William Hugh Woodin (born April 23, 1955 in Tucson ) is an American mathematician who deals with axiomatic set theory.

Woodin received his PhD in 1984 from Robert M. Solovay at the University of California, Berkeley, with a dissertation on Discontinuous Homomorphisms of C (X) and Set Theory . He's a professor at Berkeley. In 2002/03 and 2010/11 he was chairman of the mathematics department at Berkeley. He has been at Harvard University since January 2014 .

Woodin made important contributions to the program of internal models in set theory, the theory of determinacy, and large cardinals (one of which is named after him). Work by Woodin and by Donald A. Martin and John R. Steel (1989) showed connections between axioms of determinacy and axioms of large cardinal numbers, for which all three received the Karp Prize in 1988 . From his work on Ω-logic he believed to have found arguments for solvability (and even refutability) of the continuum hypothesis (CH). According to Paul Cohen and Kurt Gödel, this is independent of the Zermelo-Fraenkel axioms of set theory, but it remains open whether it cannot be proven or refuted by adding a few more, in a certain sense natural, axioms. Godel himself believed in refutability by adding axioms of large cardinal numbers. As a result, however, it became clear that these alone were not enough.

In the meantime Woodin assumes that an inner model of set theory can be constructed which has similar properties to the constructible universe of Godel (denoted by L), and in which the most important known large cardinal numbers already exist that exist in the set-theoretical universe V. . In this inner model, which he calls Ultimate L , the continuum hypothesis applies. Woodin had previously proven that it was sufficient to prove the existence of a super-compact cardinal number in such a model in order for it to contain the entire hierarchy of large cardinals, which made him optimistic about the construction of such a model. If he succeeds in the construction, he sees in it a candidate for an ideal set-theoretical universe and the addition of an axiom V = Ultimate L as a natural extension of the ZFC axioms. However, the opinion of set theorists regarding a possible extension of the ZFC axioms is divided, some like Woodin favor an axiom in which CH applies, others favor the addition of forcing axioms (like Martin's maximum ), with which many different set theoretical models are constructed in which CH does not apply.

In 1991 he showed with Matthew Foreman that the generalized continuum hypothesis can be false for any infinite cardinal number (consistency with the ZF axioms).

He has been a member of the American Academy of Arts and Sciences since 2000 .

Sy Friedman (left), Hugh Woodin, Menachem Magidor (right), Oberwolfach 2005

In 2010 he gave a plenary lecture at the International Congress of Mathematicians in Hyderabad ( Strong axioms of infinity and the search for V ). In 1986 he was invited speaker at the International Congress of Mathematicians in Berkeley ( The two faces of infinity ). In 2013 he received the first Hausdorff Medal from the European Set Theory Society. Woodin Tarski is lecturer in 2018 .

Woodin is the great-grandson of former US Treasury Secretary William Hartman Woodin .

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Individual evidence

  1. ^ John Steel What is a Woodin Cardinal? , Notices AMS 2007, PDF file
  2. ↑ After the laudation for the proof that the existence of a super compact cardinal number implies the validity of the axiom of determinacy in the smallest transitive model of Zermelo-Fraenkel set theory, which includes real numbers and all ordinal numbers.
  3. ↑ About Gödel's views, for example Martin Davis, Review of Gödel Biographies by Dawson and Casti / DePauli, Notices AMS 2001, PDF file
  4. ^ Richard Elwes: Ultimate logic . New Scientist , July 30, 2011, pp. 30-33
  5. ↑ Woodin Suitable extender models I , Journal of Mathematical Logic, Volume 10, 2010, p. 101, abstract
  6. ↑ Nathalie Wolchover To settle infinity dispute a new law of logic , Quanta Magazine, 2013, Simons Foundation
  7. ^ Book of Members. (PDF) Retrieved July 23, 2016 (English).
  8. ↑ For the work: Suitable extender models IJ Math. Log., Volume 10, 2010, pp. 101–339, Part II: Beyond omega-huge. J. Math. Log., Volume 11, 2011, pp. 115-436, which was recognized as an essential contribution to the theory of the inner model of supercompact cardinal numbers. Hausdorff Medals, ESTS
personal data
SURNAME Woodin, W. Hugh
ALTERNATIVE NAMES Woodin, William Hugh (full name)
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH April 23, 1955
PLACE OF BIRTH Tucson