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Groupwise density and related cardinals

Authors:	Andreas Blass

Institution:	(1) Mathematics Department, University of Michigan, 48109 Ann Arbor, MI, USA

Abstract:	We prove several theorems about the cardinal $\mathfrak{g}$ associated with groupwise density. With respect to a natural ordering of families of nond-ecreasing maps from to, all families of size $< \mathfrak{g}$ are below all unbounded families. With respect to a natural ordering of filters on, all filters generated by $< \mathfrak{g}$ sets are below all non-feeble filters. If $\mathfrak{u}< \mathfrak{g}$ then $\mathfrak{b}< \mathfrak{u}$ and $\mathfrak{g} = \mathfrak{d} = \mathfrak{c}$ . (The definitions of these cardinals are recalled in the introduction.) Finally, some consequences deduced from $\mathfrak{u}< \mathfrak{g}$ by Laflamme are shown to be equivalent to $\mathfrak{u}< \mathfrak{g}$ .

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