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.

0

Turn this paper into a lesson

ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.

Discussion (0)

Sign in to join the discussion.

Loading comments…