Logic Seminar

Zach NorwoodCornell University
Mad families, happy families, and generic absoluteness

Tuesday, September 18, 2018 - 2:55pm
Malott 206

Abstract: In the `70s, Mathias proved that every set in the Solovay model has the Ramsey Property, and he asked whether there were any infinite mad families in the Solovay model. In 2015, Törnquist confirmed that there are not. I will talk about a theorem (joint with Itay Neeman) that sheds light on happy families (aka "selective coideals") in the Solovay model and gives Törnquist's theorem as a corollary. I will also talk about related results in the context of determinacy, including the theorem (also joint with Itay Neeman) that under AD^+ there are no infinite mad families on the integers. If time allows, I will also talk about several interesting open questions and some more recent work.