### Additivity Properties of Topological Diagonalizations

by Bartoszynski and Shelah and Tsaban. [BShT:774]

J Symbolic Logic, 2003

In a work of Just, Miller, Scheepers and Szeptycki it was asked
whether certain diagonalization properties for sequences of open
covers are provably closed under taking finite or countable
unions. In a recent work, Scheepers proved that one of the classes
in question is closed under taking countable unions. In this paper
we show that none of the remaining classes is provably closed under
taking finite unions, and thus settle the problem. We also show that
one of these properties is consistently (but not provably) closed
under taking unions of size less than the continuum, by relating a
combinatorial version of this problem to the Near Coherence of
Filters (NCF) axiom, which asserts that the Rudin-Keisler ordering
is downward directed.

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