We construct a consistent example of a normal locally compact metacompact space which is not paracompact, answering a question of A. V. Arkhangel’skiĭ and F. Tall. An interplay between a tower in P(ω)/Fin, an almost disjoint family in , and a version of an (ω,1)-morass forms the core of the proof. A part of the poset which forces the counterexample can be considered a modification of a poset due to Judah and Shelah for obtaining a Q-set by a countable support iteration.
@article{bwmeta1.element.bwnjournal-article-fmv149i2p143bwm,
author = {Gary Gruenhage and Piotr Koszmider},
title = {The Arkhangel'ski\u\i --Tall problem: a consistent counterexample},
journal = {Fundamenta Mathematicae},
volume = {149},
year = {1996},
pages = {143-166},
zbl = {0862.54020},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv149i2p143bwm}
}
Gruenhage, Gary; Koszmider, Piotr. The Arkhangel’skiĭ–Tall problem: a consistent counterexample. Fundamenta Mathematicae, Tome 149 (1996) pp. 143-166. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv149i2p143bwm/
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