This will be a talk for the Oslo potentialism workshop, Varieties of Potentialism, to be held online via Zoom on 23 September 2020, from noon to 18:40 CEST (11am to 17:40 UK time). My talk is scheduled for 13:10 CEST (12:10 UK time). Further details about access and registration are availavle on the conference web page.

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
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