- 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
When does every definable nonempty set have a definable element?
MATHEMATICAL LOGIC QUARTERLY (12 December 2019) Full text available
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
THE MODAL LOGIC of SET-THEORETIC POTENTIALISM and the POTENTIALIST MAXIMALITY PRINCIPLES
Review of Symbolic Logic (1 January 2019)
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.