This will be a talk in the Oslo Logic Seminar. Handout here.
In this talk, I will present some early-stage work in progress on the iterative conceptions of set. In a recent booklet (itself entitled Iterative Conceptions of Set) I’ve argued that we can think more generally about the iterative conception as a way of generating sets, without committing to the Powerset operation. The booklet is rather “programmatic”, however, and leaves a lot of mathematical questions open. In this talk I’ll try to accomplish the following things:
(1.) I’ll present the rough idea I gave in the booklet.
(2.) I’ll outline one application I’m working on (a version of Steel’s multiverse programme), and the challenges I’m facing there.
(3.) I’ll present some thoughts about how one might try to extract a general notion of an “iterative conception of set”, at least model-theoretically.