A Small Ultrafilter Number at Every Singular Cardinal
Abstract
We obtain a small ultrafilter number at ω1. Moreover, we develop a version of the overlapping strong extender forcing with collapses which can keep the top cardinal inaccessible. We apply this forcing to construct a model where is the least inaccessible and V is a model of GCH at regulars, failures of SCH at singulars, and the ultrafilter numbers at all singulars are small.
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