Geodesic
The Arkhangel'skiĭ–Tall problem under Martin’s Axiom
Fundamenta Mathematicae, Tome 149 (1996) no. 3, pp. 275-285
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We show that MA$_{σ-centered}(ω_1)$ implies that normal locally compact metacompact spaces are paracompact, and that MA($ω_1$) 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. 
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Gary  Gruenhage; Piotr Koszmider. The Arkhangel'skiĭ–Tall problem under Martin’s Axiom. Fundamenta Mathematicae, Tome 149 (1996) no. 3, pp. 275-285. doi: 10.4064/fm-149-3-275-285

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