Logic Seminar
I will present Aspero and Mota's recent work in which they obtain a model of set theory which satisfies |R|>ℵ2 and in which the filter of closed unbounded subsets of ω1 has a strong combinatorial property. Specifically, in their model if Dα⊆α is closed for each α∈ω1, there is a closed unbounded E⊆ω1 such that if α is a limit ordinal, then there is an α0<α such that E∩(α0,α) is contained in or disjoint from Dα.