Natural weakenings of uniformizability of a ladder system on ω₁ are considered. It is shown that even assuming CH all the properties may be distinct in a strong sense. In addition, these properties are studied in conjunction with other properties inconsistent with full uniformizability, which we call anti-uniformization properties. The most important conjunction considered is the uniformization property we call countable metacompactness and the anti-uniformization property we call thinness. The existence of a thin, countably metacompact ladder system is used to construct interesting topological spaces: a countably paracompact and nonnormal subspace of ω₁², and a countably paracompact, locally compact screenable space which is not paracompact. Whether the existence of a thin, countably metacompact ladder system is consistent is left open. Finally, the relation between the properties introduced and other well known properties of ladder systems, such as ♣, is considered.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm181-3-1,
author = {Todd Eisworth and Gary Gruenhage and Oleg Pavlov and Paul Szeptycki},
title = {Uniformization and anti-uniformization properties of ladder systems},
journal = {Fundamenta Mathematicae},
volume = {184},
year = {2004},
pages = {189-213},
zbl = {1051.03034},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm181-3-1}
}
Todd Eisworth; Gary Gruenhage; Oleg Pavlov; Paul Szeptycki. Uniformization and anti-uniformization properties of ladder systems. Fundamenta Mathematicae, Tome 184 (2004) pp. 189-213. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm181-3-1/