- Professor of Logic, Faculty of Philosophy
- Affiliate Faculty, Mathematics Institute
- Sir Peter Strawson Fellow in Philosophy, University College
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
A model of the generic Vopenka principle in which the ordinals are not Mahlo
ARCHIVE FOR MATHEMATICAL LOGIC issue 1-2 volume 58 page 245-265 (February 2019) Full text available
Logic and Logical Philosophy issue 3 volume 25 page 285-308 (1 September 2016)
Superstrong and other large cardinals are never Laver indestructible
ARCHIVE FOR MATHEMATICAL LOGIC issue 1-2 volume 55 page 19-35 (February 2016) Full text available
Is the Dream Solution of the Continuum Hypothesis Attainable?
NOTRE DAME JOURNAL OF FORMAL LOGIC issue 1 volume 56 page 135-145 (2015) Full text available
I conduct research broadly in mathematical and philosophical logic, particularly set theory, with a focus on the mathematics and philosophy of the infinite. My work spans topics from forcing and large cardinals, second-order set theory, infinitary computability and infinitary game theory, such as the mathematics of infinite chess. Much of my work involves the interaction of mathematical issues with philosophical concerns, such as those arising in the emerging debate on pluralism in the philosophy of set theory, including the mathematical questions to which they lead, such as my work on the modal logic of forcing and set-theoretic geology and, more recently, the various manifestations of potentialism in mathematics.