W. Hugh Woodin
William Hugh Woodin ( born April 23, 1955 in Tucson ) is an American mathematician who is engaged in axiomatic set theory.
Woodin received his doctorate in 1984 with Robert M. Solovay at the University of California, Berkeley (Discontinuous homomorphisms of C (X) and Set Theory ). He is a professor at Berkeley. 2002/ 03 and 2010/11, he was chairman of the Mathematics Department at Berkeley. From January 2014 he is at Harvard University.
Woodin made important contributions to the program of inner models of set theory, theory of determinacy and large cardinal numbers ( one of which is named after him). Work of Woodin and Donald A. Martin and John R. Steel ( 1989) showed connections between determinacy axioms and axioms of large cardinals, for which all three of the 1988 Karp Prize received. From his work on logic he believed arguments for solvability (and even falsifiability ) of the continuum hypothesis (CH) to have found. This is independent of the Zermelo -Fraenkel axioms of set theory by Paul Cohen and Kurt Gödel, remains open but if it is not by adding some other " natural" axioms but provable or refutable. Godel himself believed in a rebuttable by adding axioms of large cardinals. As a result, however, showed that these alone are not enough.
Meanwhile, goes Woodin assume that an inner model of set theory can be constructed, which has similar properties as the constructible universe Godel (L ), and exist in the already almost all known large cardinals that exist in the set-theoretic universe V. In this internal model, which he calls Ultimate L, the continuum hypothesis is true. Previously Woodin 2010 had proved that it is sufficient to prove the existence of a supercompact cardinal in such a model so that it contains the entire hierarchy of large cardinal numbers, which made him optimistic with regard to the construction of such Ultimate L model. If he succeeds, the design proposed is a candidate for an ideal set-theoretical universe and the addition of an axiom V = L Ultimate as a natural extension of ZFC axioms. The opinion of the quantity theorists of a possible extension of ZFC axioms with respect but not split, some favoritisieren as Woodin an axiom V = Ultimate L ( in which CH is true ), other favoritisieren the addition of forcing axioms ( as Martin's maximum), with where many different set-theoretical models can be constructed in which CH is not considered.
In 1991, he exhibited with Matthew Foreman that the generalized continuum hypothesis, for every infinite cardinal number may be incorrect (consistency with the ZF axioms ).
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 ).
Woodin is the great-grandson of former U.S. Treasury Secretary William Hartman Woodin.
Writings
- The axiom of determinacy, forcing axioms, and the Nonstationary Ideal, de Gruyter, 1999 ISBN 311015708X