Speaker: Eben Blaisdell

Title: Unprovability of Unprovability of … of Unprovability, Proven in the Multiverse

Abstract: Godel’s first incompleteness theorem shows the existence of an arithmetical statement that is true but unprovable.  One could playfully ask if there is a true arithmetical statement which is unprovable, but whose unprovability is unprovable.  What about unprovability of the unprovability of the unprovability, and so on?  In this talk (by black-boxing some major theorems) we give a characterization of the existence of such statements.  On the way, we naturally arrive at some very fun logic, including Kripke semantics of modal logic, a ‘multiversal’ logic.  There we will find that a core metatheorem about provability corresponds to an induction principle for a certain class of graphs.