W. Hugh Woodin
Encyclopedia
William Hugh Woodin is an American mathematician and set theorist
at University of California, Berkeley
. He has made many notable contributions to the theory of inner model
s and determinacy
. A type of large cardinal, the Woodin cardinal
, bears his name.
, Woodin earned his Ph.D.
from the University of California, Berkeley in 1984 under Robert M. Solovay
. His dissertation title was Discontinuous Homomorphisms of C(Omega) and Set Theory. He served as chair of the Berkeley mathematics department for the 2002-2003 academic year. Woodin is a managing editor of the Journal of Mathematical Logic
. He was elected a Fellow of the American Academy of Arts and Sciences
in 2000.
He is the great-grandson of William Hartman Woodin
, former Secretary of the Treasury
.
is either undecidable or false in the sense of Mathematical Platonism. Woodin criticizes this view arguing that it leads to a counterintuitive reduction in which all truths in the set theoretical universe can be decided from a small part of it. He claims that these and related mathematical results lead (intuitively) to the conclusion that Continuum Hypothesis has a truth value and the Platonistic approach is reasonable.
Woodin now predicts that there should be a way of constructing an inner model for almost all known large cardinals which he calls the Ultimate L and which would have similar properties as Gödel's constructible universe
. In particular, the Continuum Hypothesis would be true in this universe.
Set theory
Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...
at University of California, Berkeley
University of California, Berkeley
The University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...
. He has made many notable contributions to the theory of inner model
Inner model
In mathematical logic, suppose T is a theory in the languageL = \langle \in \rangleof set theory.If M is a model of L describing a set theory and N is a class of M such that \langle N, \in_M, \ldots \rangle...
s and determinacy
Determinacy
In set theory, a branch of mathematics, determinacy is the study of under what circumstances one or the other player of a game must have a winning strategy, and the consequences of the existence of such strategies.-Games:...
. A type of large cardinal, the Woodin cardinal
Woodin cardinal
In set theory, a Woodin cardinal is a cardinal number λ such that for all functionsthere exists a cardinal κ In set theory, a Woodin cardinal is a cardinal number λ such that for all functions...
, bears his name.
Biography
Born in Tucson, ArizonaArizona
Arizona ; is a state located in the southwestern region of the United States. It is also part of the western United States and the mountain west. The capital and largest city is Phoenix...
, Woodin earned his Ph.D.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
from the University of California, Berkeley in 1984 under Robert M. Solovay
Robert M. Solovay
Robert Martin Solovay is an American mathematician specializing in set theory.Solovay earned his Ph.D. from the University of Chicago in 1964 under the direction of Saunders Mac Lane, with a dissertation on A Functorial Form of the Differentiable Riemann–Roch theorem...
. His dissertation title was Discontinuous Homomorphisms of C(Omega) and Set Theory. He served as chair of the Berkeley mathematics department for the 2002-2003 academic year. Woodin is a managing editor of the Journal of Mathematical Logic
Journal of Mathematical Logic
The Journal of Mathematical Logic was established in 2001 and is published by World Scientific. It covers the field of mathematical logic and its applications.- Abstracting and indexing :The journal is abstracted and indexed in:...
. He was elected a Fellow of the American Academy of Arts and Sciences
American Academy of Arts and Sciences
The American Academy of Arts and Sciences is an independent policy research center that conducts multidisciplinary studies of complex and emerging problems. The Academy’s elected members are leaders in the academic disciplines, the arts, business, and public affairs.James Bowdoin, John Adams, and...
in 2000.
He is the great-grandson of William Hartman Woodin
William Hartman Woodin
William Hartman Woodin was a U.S. industrialist. He served as the Secretary of Treasury under Franklin Roosevelt in 1933.Woodin was closely involved in Jackson and Woodin Manufacturing Company...
, former Secretary of the Treasury
United States Secretary of the Treasury
The Secretary of the Treasury of the United States is the head of the United States Department of the Treasury, which is concerned with financial and monetary matters, and, until 2003, also with some issues of national security and defense. This position in the Federal Government of the United...
.
Work
He has done work on the theory of generic multiverses and related concept of Ω-logic which suggested an argument that the Continuum HypothesisContinuum hypothesis
In mathematics, the continuum hypothesis is a hypothesis, advanced by Georg Cantor in 1874, about the possible sizes of infinite sets. It states:Establishing the truth or falsehood of the continuum hypothesis is the first of Hilbert's 23 problems presented in the year 1900...
is either undecidable or false in the sense of Mathematical Platonism. Woodin criticizes this view arguing that it leads to a counterintuitive reduction in which all truths in the set theoretical universe can be decided from a small part of it. He claims that these and related mathematical results lead (intuitively) to the conclusion that Continuum Hypothesis has a truth value and the Platonistic approach is reasonable.
Woodin now predicts that there should be a way of constructing an inner model for almost all known large cardinals which he calls the Ultimate L and which would have similar properties as Gödel's constructible universe
Constructible universe
In mathematics, the constructible universe , denoted L, is a particular class of sets which can be described entirely in terms of simpler sets. It was introduced by Kurt Gödel in his 1938 paper "The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis"...
. In particular, the Continuum Hypothesis would be true in this universe.
External links
- Home page at University of California, Berkeley
- Woodin's plenary talk at the 2010 International Congress of Mathematicians
- Incompatible Ω-Complete Theories (with Peter KoellnerPeter KoellnerPeter Koellner is the John L. Loeb Associate Professor of the Humanities at Harvard University. He received his Ph.D from MIT in 2003. His main areas of research are mathematical logic, specifically set theory, and philosophy of mathematics, philosophy of physics, analytic philosophy, and...
), Journal of Symbolic LogicJournal of Symbolic LogicThe Journal of Symbolic Logic is a peer-reviewed mathematics journal published quarterly by Association for Symbolic Logic.Founded in 1936, the journal publishes articles on mathematical logic....
, Volume 74, Issue 4 (2009), 1155-1170.http://projecteuclid.org/euclid.jsl/1254748685.