This is a talk in the Logic Supergroup Early Career Researcher Workshop on 2021 October 14.

[slides]

Set-theoretic potentialism is the view that the universe of sets is never fully completed but is only given potentially. There are multiple varieties of this viewpoint, based on different views on just how this gradual unfolding of sets occurs. Tools from modal logic have been applied to more finely understand the commitments of and distinctions between different varieties of set-theoretic potentialism. In recent joint work with Neil Barton we extended this analysis to study class-theoretic potentialism, the view that proper classes are given potentially (while the sets may or may not be fixed). In this talk I will survey some of the prior work on the mathematics of set-theoretic potentialism and present some of our work on class-theoretic potentialism.