# Sh:774

• Bartoszyński, T., Shelah, S., & Tsaban, B. (2003). Additivity properties of topological diagonalizations. J. Symbolic Logic, 68(4), 1254–1260.
• Abstract:
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.
• Version 2004-02-24_11 (17p) published version (7p)
Bib entry
@article{Sh:774,
author = {Bartoszy{\'n}ski, Tomek and Shelah, Saharon and Tsaban, Boaz},
title = {{Additivity properties of topological diagonalizations}},
journal = {J. Symbolic Logic},
fjournal = {The Journal of Symbolic Logic},
volume = {68},
number = {4},
year = {2003},
pages = {1254--1260},
issn = {0022-4812},
mrnumber = {2017353},
mrclass = {03E35 (03E04 03E55 03E75 54H05)},
doi = {10.2178/jsl/1067620185},
note = {\href{https://arxiv.org/abs/math/0112262}{arXiv: math/0112262}},
arxiv_number = {math/0112262},
keyword = {Menger property, Hurewicz property, selection principles, additivity numbers, Rudin-Keisler ordering, near coherence of
filters}
}