Logic Seminar

Justin MooreCornell University
The combinatorics of the club filter and the size of the continuum

Wednesday, February 1, 2017 - 4:00pm
Malott 206

I will present Aspero and Mota's recent work in which they obtain a model of set theory which satisfies \(|\mathbb{R}| > \aleph_2\) and in which the filter of closed unbounded subsets of \(\omega_1\) has a strong combinatorial property. Specifically, in their model if \(D_\alpha \subseteq \alpha\) is closed for each \(\alpha \in \omega_1\), there is a closed unbounded \(E \subseteq \omega_1\) such that if \(\alpha\) is a limit ordinal, then there is an \(\alpha_0 < \alpha\) such that \(E \cap (\alpha_0,\alpha)\) is contained in or disjoint from \(D_\alpha\).