# Giorgio Audrito, PhD 2016, University of Torino

Dr. Giorgio Audrito has successfully defended his dissertation, “Generic large cardinals and absoluteness,” at the University of Torino under the supervision of Matteo Viale.

The dissertation Examing Board consisted of myself (serving as Presidente), Alessandro Andretta and Sean Cox.  The defense took place March 2, 2016.

The dissertation was impressive, introducing (in joint work with Matteo Viale) the iterated resurrection axioms $\text{RA}_\alpha(\Gamma)$ for a forcing class $\Gamma$, which extend the idea of the resurrection axioms from my work with Thomas Johnstone, The resurrection axioms and uplifting cardinals, by making successive extensions of the same type, forming the resurrection game, and insisting that that the resurrection player have a winning strategy with game value $\alpha$. A similar iterative game idea underlies the $(\alpha)$-uplifting cardinals, from which the consistency of the iterated resurrection axioms can be proved. A final chapter of the dissertation (joint with Silvia Steila), develops the notion of $C$-systems of filters, generalizing the more familiar concepts of extenders and towers.

# Boldface resurrection and the strongly uplifting cardinals, the superstrongly unfoldable cardinals and the almost-hugely unfoldable cardinals, BEST 2014

I will speak at the BEST conference, which is held as a symposium in the much larger 95th Annual Meeting of the American Association for the Advancement of Science, at the University of California at Riverside, June 18-20, 2014.

This talk will be for specialists in the BEST symposium.

Abstract.  I shall introduce several new large cardinal concepts, namely, the strongly uplifting cardinals, the superstrongly unfoldable cardinals and the almost-hugely unfoldable cardinals, and prove their tight connection with one another — actually, they are equivalent! — as well as their equiconsistency with several natural instances of the boldface resurrection axiom, such as the boldface resurrection axiom for proper forcing.  This is joint work with Thomas A. Johnstone.

I am also scheduled to give a plenary General Pubic Lecture, entitled Higher infinity and the foundations of mathematics, as a part of the larger AAAS program, to which the general public is invited.