Set theory workshop
Sherwood Hachtman
UIC
Forcing analytic determinacy
Abstract: The earliest-known tight connection between determinacy and large cardinals is the theorem of Martin and Harrington that $\Sigma^1_1$ determinacy is equivalent to the existence of $0^{\#}$. All known proofs of the forward implication go through Jensen's Covering Lemma; Harrington asked whether the theorem can be proved just in second-order arithmetic. We discuss progress on Harrington's question, building in particular on work of Cheng and Schindler showing that the standard proofs of Harrington's theorem cannot be carried out in any system substantially weaker than fourth-order arithmetic. We also describe a connection with the proper class games recently described by Gitman and Hamkins.
Thursday October 20, 2016 at 2:00 PM in SEO 636