William Hugh Woodin (born April 23, 1955) is an American mathematician at
Harvard University
Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyma ...
specializing in
set theory
Set theory is the branch of mathematical logic that studies Set (mathematics), sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory – as a branch of mathema ...
. He has made many notable contributions to the theory of
inner models and
determinacy. A type of
large cardinals, the
Woodin cardinals, bears his name. In 2023, he was elected to the
National Academy of Sciences
The National Academy of Sciences (NAS) is a United States nonprofit, NGO, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the ...
.
Biography
Born in
Tucson,
Arizona
Arizona is a U.S. state, state in the Southwestern United States, Southwestern region of the United States, sharing the Four Corners region of the western United States with Colorado, New Mexico, and Utah. It also borders Nevada to the nort ...
, 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(Ω) and Set Theory''. He served as
chair
A chair is a type of seat, typically designed for one person and consisting of one or more legs, a flat or slightly angled seat and a back-rest. It may be made of wood, metal, or synthetic materials, and may be padded or upholstered in vario ...
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
The American Academy of Arts and Sciences (The Academy) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and other ...
in 2000.
He is the great-grandson of
William Hartman Woodin, former
Secretary of the Treasury
The United States secretary of the treasury is the head of the United States Department of the Treasury, and is the chief financial officer of the federal government of the United States. The secretary of the treasury serves as the principal a ...
.
Work
Woodin's earliest mathematical work concerned a connection between set theory and the theory of
Banach algebras. In the 1980s he made major contributions in the study of the
Axiom of Determinacy (AD) via
inner model theory, culminating in determining the
precise
consistency strength of AD relative to the standard
large cardinal hierarchy.
Woodin has done work on the theory of generic multiverses and the related concept of
Ω-logic, which suggested an argument that the
continuum hypothesis 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 the continuum hypothesis has a
truth value
In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values ('' true'' or '' false''). Truth values are used in ...
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.
Honors
In 2008, Woodin held the
Gödel Lecture titled ''The Continuum Hypothesis, the Conjecture, and the inner model problem of one supercompact cardinal.''
In 2018, he was the
Tarski lecturer.
See also
*
AD+
References
External links
*
*
Home pageat University of California, Berkeley
Woodin's plenary talk at the 2010 International Congress of MathematiciansIncompatible Ω-Complete Theories
(with Peter Koellner), ''Journal of Symbolic Logic
The '' Journal of Symbolic Logic'' is a peer-reviewed mathematics journal published quarterly by Association for Symbolic Logic. It was established in 1936 and covers mathematical logic. The journal is indexed by '' Mathematical Reviews'', Zent ...
'', Volume 74, Issue 4 (2009), 1155–117
{{DEFAULTSORT:Woodin, W. Hugh
American logicians
20th-century American mathematicians
21st-century American mathematicians
1955 births
Living people
Fellows of the American Academy of Arts and Sciences
University of California, Berkeley alumni
University of California, Berkeley faculty
Harvard University Department of Mathematics faculty
Harvard University Department of Philosophy faculty
Set theorists
Hausdorff Medal winners
Members of the United States National Academy of Sciences