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STABLE ORDERED UNION ULTRAFILTERS AND cov
$\left( \mathcal{M} \right) < \mathfrak{c}$
Published online by Cambridge University Press: 03 April 2019
Abstract
A union ultrafilter is an ultrafilter over the finite subsets of ω that has a base of sets of the form ${\text{FU}}\left( X \right)$, where X is an infinite pairwise disjoint family and
${\text{FU}}(X) = \left\{ {\bigcup {F|F} \in [X]^{ < \omega } \setminus \{ \emptyset \} } \right\}$. The existence of these ultrafilters is not provable from the
$ZFC$ axioms, but is known to follow from the assumption that
${\text{cov}}\left( \mathcal{M} \right) = \mathfrak{c}$. In this article we obtain various models of
$ZFC$ that satisfy the existence of union ultrafilters while at the same time
${\text{cov}}\left( \mathcal{M} \right) = \mathfrak{c}$.
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- Copyright © The Association for Symbolic Logic 2019
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