# W. Hugh Woodin

**William Hugh Woodin** (born April 23, 1955) is an American mathematician and set theorist at Harvard University. He has made many notable contributions to the theory of inner models and determinacy. A type of large cardinal, the Woodin cardinal, bears his name.

W. Hugh Woodin | |
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Hugh Woodin in 1994 (photo by George Bergman) | |

Born | Tucson, Arizona, U.S. | April 23, 1955

Nationality | American |

Alma mater | University of California, Berkeley |

Scientific career | |

Fields | Mathematics |

Institutions | University of California, Berkeley California Institute of Technology Harvard University |

Doctoral advisor | Robert M. Solovay |

Doctoral students | Joel David Hamkins Gregory Hjorth |

## Biography

Born in Tucson, Arizona, 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.[1]

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

## Work

He 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 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.[2]

## See also

## References

- "Book of Members, 1780–2010: Chapter W" (PDF). American Academy of Arts and Sciences. Retrieved June 3, 2011.
- Wolchover, Natalie (26 November 2013). "To Settle Infinity Dispute, a New Law of Logic".
*Quanta Magazine*.

## External links

- W. Hugh Woodin at the Mathematics Genealogy Project
- Woodin, W. Hugh (2010).
*The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal*. Walter de Gruyter. ISBN 978-3-11-019702-0. OCLC 605013810. - Home page at University of California, Berkeley
- Woodin's plenary talk at the 2010 International Congress of Mathematicians
- Incompatible Ω-Complete Theories (with Peter Koellner),
*Journal of Symbolic Logic*, Volume 74, Issue 4 (2009), 1155–1170..