Negating the Galvin property

Abstract

We investigate Galvin's property, a striking feature of the filter of closed unbounded subsets of an infinite cardinal. In particular, we continue the work of Abraham and Shelah (J. Symbolic Logic 51 (1986), no. 1, 180–189) by developing new methods to handle singular cardinals. In addition, the paper explores some new strengthenings of Galvin's property and analyzes their connections with other classical properties of filters.

On Cohen and Prikry Forcing Notions

“…In [1], Abraham and Shelah constructed a model where fails for a regular . Garti [13, 14] and later together with the first author and Poveda [4] continued the investigation of the Galvin property for the club filter. The Galvin property for -complete ultrafilters over a measurable cardinal was used recently in [7, 18].…”