On densities of box products

AbstractWe construct two universes V1, V2 satisfying the following GCH below ℵω, 2ℵω = ℵω + 2 and the topological density of the space ℵω2 with ℵ0 box product topology d<ℵ1 (ℵω) is ℵω + 1 in V1 and ℵω + 2 in V2. Further related results are discussed as well

Global square and mutual stationarity at the ℵn

AbstractWe give the proof of a theorem of Jensen and Zeman on the existence of a global □ sequence in the Core Model below a measurable cardinal κ of Mitchell order (oM(κ)) equal to κ++, and use it to prove the following theorem on mutual stationarity at ℵn.Let ω1 denote the first uncountable cardinal of V and set Cof(ω1) to be the class of ordinals of cofinality ω1. TheoremIf every sequence (Sn)n<ω of stationary sets Sn⊆Cof(ω1)∩ℵn+2, is mutually stationary, then there is an inner model with infinitely many inaccessibles (κn)n<ω so that for every mthe class of measurables λ with oM(λ)≥κm is, in V, stationary in κn for all n>m. In particular, there is such a model in which for all sufficiently large m<ω, the class of measurables λ with oM(λ)≥ωm is, in V, stationary below ℵm+2

Set Theory

This workshop included selected talks on pure set theory and its applications, simultaneously showing diversity and coherence of the subject