Professor John Krueger invites you to attend the Masters project defense of Thomas Gilton next Wednesday, March 26th, at 3:30 pm in GAB 461. Cookies and coffee will be served in GAB 472 following this event.
"$I[ω2]$ and Adequate Set Forcing"
Abstract: In this talk we introduce Shelah's approachability ideal I[ω 2]. We sketch a proof by William Mitchell that it is consistent from a Greatly Mahlo cardinal that I[ω 2] is the nonstationary ideal on cf(ω 1). A key idea of the proof is to use side conditions forcing, which we formulate using John Krueger's notion of an adequate set of models. We also discuss the theory of strongly proper forcing posets, another key ingredient of Mitchell's proof. The talk will conclude with an approximation of Mitchell's forcing poset.