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# On the Hereditary Paracompactness of Locally Compact, Hereditarily Normal Spaces

• Paul Larson,
Department of Mathematics, University of Toronto, Toronto, ON M5S 3G3
• Franklin D. Tall,
Department of Mathematics, University of Toronto, Toronto, ON M5S 3G3
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## Abstract

We establish that if it is consistent that there is a supercompact cardinal, then it is consistent that every locally compact, hereditarily normal space which does not include a perfect pre-image of $\omega_1$ is hereditarily paracompact.
 Keywords: locally compact, hereditarily normal, paracompact, Axiom R, PFA$^{++}$
 MSC Classifications: 54D35 - Extensions of spaces (compactifications, supercompactifications, completions, etc.) 54D15 - Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.) 54D20 - Noncompact covering properties (paracompact, Lindelof, etc.) 54D45 - Local compactness, $\sigma$-compactness 03E65 - Other hypotheses and axioms 03E35 - Consistency and independence results

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