Event Detail

A Σ2 statement ϕ is called possible if, for every ordinal alpha, ϕ holds in a generic extension which preserves Vα (set of sets of rank less than α). Woodin’s Σ2 potentialist principle is the statement that every possible Σ2 sentence is true. In a joint work with Omer Ben-Neria and Gabriel Goldberg, we proved that a supercompact cardinal suffices to force the potentialist principle. Also, the principle implies the consistency of a Woodin cardinal. In the talk, we will present the principle and sketch the proof that it can be forced from a supercompact cardinal.