Normality Versus Paracompactness inLocally Compact Spaces

Dow, Alan ; Tall, Franklin D.

Canadian journal of mathematics, Tome 70 (2018) no. 1, pp. 74-96

Résumé

This note provides a correct proof of the result claimed by the second author that locally compact normal spaces are collectionwise Hausdorff in certain models obtained by forcing with a coherent Souslin tree. A novel feature of the proof is the use of saturation of the non-stationary ideal on ${{\omega }_{1}}$ , as well as of a strong form of Chang's Conjecture. Together with other improvements, this enables the consistent characterization of locally compact hereditarily paracompact spaces as those locally compact, hereditarily normal spaces that do not include a copy of ${{\omega }_{1}}$ .

Détail

DOI : 10.4153/CJM-2017-006-x

Mots-clés : 54A35, 54D20, 54D45, 03E35, 03E50, 03E55, 03E57, normal, paracompact, locally compact, countably tight, collectionwise Hausdorff, forcing with a coherent Souslin tree, Martin's Maximum, PFA(S)[S], Axiom R, moving off property

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