I shall talk about the tension between resurrection and large cardinals at the IMS Graduate Summer School in Logic at the National University of Singapore, 7th of July 2022.
Abstract. The mantle is the intersection of all ground models of the universe. By a result of Usuba, the mantle is a ground in the presence of an extendible cardinal. In his recent work, Goldberg argues that this large cardinal hypothesis cannot be weakened. I shall discuss these results in the context of the axiom of resurrection, outlining a plan for my research project. This is a project supervised by W. Hugh Woodin.