My main research interest lies in mathematical and philosophical logic, particularly set theory, with a focus on the mathematics and philosophy of the infinite. I have worked particularly with forcing and large cardinals, those strong axioms of infinity, and have investigated the interaction of these two central set-theoretic concepts.  I have worked in the theory of infinitary computability, introducing (with A. Lewis and J. Kidder) the theory of infinite time Turing machines, as well as in the theory of infinitary utilitarianism and, more recently, infinite chess.  My work on the automorphism tower problem lies at the intersection of group theory and set theory.  Recently, I am preoccupied with various mathematical and philosophical issues surrounding the set-theoretic multiverse, engaging with the emerging debate on pluralism in the philosophy of set theory, as well as the mathematical questions to which they lead, such as my work on the modal logic of forcing and set-theoretic geology.  I was interviewed by Richard Marshall at 3:AM Magazine about my work (and see other mentions of me in the news).  Please edit my Wikipedia entry.

Starting 2022, I am now the John Cardinal O’Hara Professor of Logic at the University of Notre Dame.

From 2018 to 2022, I was Professor of Logic at Oxford University and the Sir Peter Strawson Fellow at University College Oxford.

Before that, my permanent position for many years was Professor at The City University of New York, at the Graduate Center of CUNY and the College of Staten Island of CUNY.

I have also held various academic faculty positions at other universities and institutions around the world.

For detailed information, please see my Curriculum Vita.


  • University of Notre Dame, beginning January 2022
  • Oxford University, 2018 – 2022
  • The City University of New York, 1995-2018
    College of Staten Island of CUNY
    Distinguished Professor, 2020.
  • Isaac Newton Institute for Mathematical Sciences, Cambridge, U.K.
    • Visiting Fellow, August–September, 2015
    • Visiting Fellow, March–April, June, 2012
  • New York University
    • Visiting Professor of Philosophy, January-June, 2015
    • Visiting Professor of Philosophy, July-December, 2011
  • Fields Institute, Toronto, Scientific Researcher, August 2012
  • University of Vienna, Kurt Gödel Research Center, Guest Professor, June, 2009.
  • Universiteit van Amsterdam, Institute for Logic, Language & Computation
    • NWO Bezoekersbeurs Visiting Researcher, June–August 2005, June 2006.
    • Visiting Professor, April–August 2007.
  • Universität Münster, Institut für mathematische Logik, Germany, Mercator-Gastprofessor, DFG, May–August 2004.
  • Georgia State University, Associate Professor of Mathematics and Statistics, 2002–2003.
  • Carnegie Mellon University, Visiting Associate Professor of Mathematics, 2000–2001.
  • Kobe University, Japan, JSPS Research Fellow, Jan–Dec 1998.
  • Univ. California at Berkeley, Visiting Assistant Professor of Mathematics, 1994–1995.
  • More information about my appointments


  • Ph.D. in mathematics, 1994, University of California at Berkeley
  • C.Phil., 1991, University of California at Berkeley
  • B.S. in mathematics (with honor), 1988, California Institute of Technology
  • M.A. by resolution, September 2018, Oxford University

Selected Major grants and awards


I am active on MathOverflow, and my contributions there (see my profile) have earned the top-rated reputation score.

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