This will be a talk for the Panglobal Algebra and Logic seminar at the University of Colorado Boulder, March 12, 2025, 3:30pm MDT

The talk will be available live on Zoom. Contact the organizers for access.

Abstract. I shall introduce and describe the subject of modal model theory, in which one studies a mathematical structure within a class of similar structures under an extension concept, giving rise to mathematically natural notions of possibility and necessity, a form of mathematical potentialism. We study the class of all graphs, or all groups, all fields, all orders, or what have you; a natural case is the class of all models of a fixed first-order theory. In this talk, I shall describe some of the resulting elementary theory, particularly the remarkable expressive power of modal graph theory. This is joint work with my Oxford student Wojciech Wołoszyn.