We show that MA implies that normal locally compact metacompact spaces are paracompact, and that MA() implies normal locally compact metalindelöf spaces are paracompact. The latter result answers a question of S. Watson. The first result implies that there is a model of set theory in which all normal locally compact metacompact spaces are paracompact, yet there is a normal locally compact metalindelöf space which is not paracompact.
@article{bwmeta1.element.bwnjournal-article-fmv149i3p275bwm,
author = {Gary Gruenhage and Piotr Koszmider},
title = {The Arkhangel'ski\u\i --Tall problem under Martin's Axiom},
journal = {Fundamenta Mathematicae},
volume = {149},
year = {1996},
pages = {275-285},
zbl = {0855.54006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv149i3p275bwm}
}
Gruenhage, Gary; Koszmider, Piotr. The Arkhangel'skiĭ–Tall problem under Martin’s Axiom. Fundamenta Mathematicae, Tome 149 (1996) pp. 275-285. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv149i3p275bwm/
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