Philosophy of Mathematics seminar

Chris Scambler, Oxford

Axiomatic Potentialism  

In this talk I will discuss some logical questions regarding the relation between modal axiom systems for set-theoretic potentialism and more familiar axiom systems in purely quantificational languages. I’ll start by sketching extant results relating axiomatic systems for ‘height’ potentialism to good old-fashioned ZFC. I’ll then turn to some new, analogous results I have attained that relate combined systems for ‘height and width’ potentialism to second order arithmetic extended by so-called ‘topological regularity’ axioms. I will also try to say something about what I take the significance of these results to be.