Joel David Hamkins — Set-theoretic and arithmetic potentialism: the state of current developments

This was a plenary talk for the Chinese Annual Conference on Mathematical Logic (CACML 2020), Nankai University, 13-15 November 2020.

Abstract. Recent years have seen a flurry of mathematical activity in set-theoretic and arithmetic potentialism, in which we investigate a collection of models under various natural extension concepts. These potentialist systems enable a modal perspective—a statement is possible in a model, if it is true in some extension, and necessary, if it is true in all extensions. We consider the models of ZFC set theory, for example, with respect to submodel extensions, rank-extensions, forcing extensions and others, and these various extension concepts exhibit different modal validities. In this talk, I shall describe the state of current developments, including the most recent tools and results.

[GrothenDitQue]

Aaaah perfect! I had to quit in the middle, and had given up the search of the recording on the CACML website x)

[LaureanoLuna]

5:15 That is a bit baffling:: The mximality principle is not the (characteristic) S5 axiom (as Hamkins seems to say) but the Brouwerian axiom, which is weaker (at least given T and in the absence of modal collapse)). Or what have I missed?