The Arkhangel'skiĭ–Tall problem under Martin’s Axiom

We show that MA${\displaystyle \_\{\sigma -centered\}\left({\omega }_1\right)}$ implies that normal locally compact metacompact spaces are paracompact, and that MA(${\displaystyle {\omega }_1}$) 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.