This is a talk in the Leeds Models and Sets Seminar on 2022 March 29.
Set-theoretic potentialism is the view that the universe of sets is never fully completed but is only given potentially. Tools from modal logic have been applied to understand the mathematics of potentialism. In recent work, Neil Barton and I extended this analysis to 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 results from set-theoretic potentialism. After seeing how the tools apply in that context I will then discuss our work in the class-theoretic context.