When countably paracompact, locally compact, screenable spaces are paracompact (Q579647)

The paper is closely related with the open question due to Arkhangel'skij and Tall whether every normal, locally compact, metacompact space is paracompact. It is known that every normal, locally compact, screenable space is paracompact and, moreover, a countably paracompact, locally compact, screenable space is paracompact under the assumption \(V=L\). The aim of the author is to prove that one can replace the assumption V\(=L\) by R\(+MA_{\omega_ 1}\) in the above assertion, where both R and \(MA_{\omega_ 1}\) follow from Martin's maximum or some strengthening of the PFA.