Dense families of countable sets below $c$

Soukup, Lajos (2010) Dense families of countable sets below $c$. (Unpublished)

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Abstract

We show that it is consistent that is as large as you wish, and for each uncountable cardinal , there are a set and a family with such that
(a) for each ,
(b) for each there is with ,
and so
(i) there is an almost disjoint family with size and chromatic number ,
(ii) there is a locally compact, locally countable space with cardinality spectrum .

Item Type: Research Paper almost disjoint, refinement, chromatic number , cardinality spectrum, Cohen reals, 54A35 Consistency and independence results54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets)03E35 Consistency and independence results Research Divisions > Set theory and general topology 02 Apr 2010 11:18

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