# The tension between large cardinals and resurrection, Cambridge March 2023

I shall give a short talk about the tension between the strong axioms of infinity and resurrection. This time at the Set Theory in The United Kingdom meeting at the University of Cambridge, 7th of March 2023.

If time permits, I shall sketch a proof of the failure of necessary $\Pi_3$-resurrection.

Abstract. Usuba proved that the mantle is a ground in the presence of an extendible cardinal. And by a recent result of Goldberg, this large cardinal hypothesis cannot be weakened. But my recent work (in progress) on resurrection principles suggests that, at heart, Usuba’s theorem is not about consistency strength. This is a project supervised by W. Hugh Woodin.

(Edited on 12 March to fix a typo.)