Boris Zilber (University of Oxford) – From Model Theory to Foundations of Physics

Model Theory is having an increasing impact in research in classical areas of mathematics, ranging from Complex Geometry through Number Theory to Combinatorics. In this talk I begin by discussing its potential applications in Foundations of Physics and subsequently  present some results in this direction. Among these, I will explain how Hilbert-space axiomatisation of quantum physics is in effect an axiomatisation in the language of Continuous Logic. In particular, I prove that in this interpretation Dirac - von Neumann axioms of quantum mechanics admit approximate models with (very large) finite universes.