caa a22 4500 465743587 CHVBK 20180323111814.0 cr unu---uuuuu 170327e19900101xx s 000 0 eng 10.1007/BF01793782 doi (NATIONALLICENCE)springer-10.1007/BF01793782 Blass Andreas Mathematics Department, University of Michigan, 48109, Ann Arbor, MI, USA aut Groupwise density and related cardinals [Elektronische Daten] [Andreas Blass] 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 fromω toω, all families of size $$< \mathfrak{g}$$ are below all unbounded families. With respect to a natural ordering of filters onω, 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 $$\mathfrak{u}< \mathfrak{g}$$ . Springer-Verlag, 1990 Archive for Mathematical Logic Springer-Verlag 30/1(1990-01-01), 1-11 0933-5846 30:1<1 1990 30 153 https://doi.org/10.1007/BF01793782 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01793782 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Blass Andreas Mathematics Department, University of Michigan, 48109, Ann Arbor, MI, USA aut NATIONALLICENCE 773 0- Archive for Mathematical Logic Springer-Verlag 30/1(1990-01-01), 1-11 0933-5846 30:1<1 1990 30 153 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer