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PFA(S)[S]: More Mutually Consistent Topological Consequences of PFA and V = L

Published online by Cambridge University Press:  20 November 2018

Franklin D. Tall
Franklin D. Tall*
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4 email: f.tall@utoronto.ca
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Abstract

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Extending the work of Larson and Todorcevic, we show that there is a model of set theory in which normal spaces are collectionwise Hausdorff if they are either first countable or locally compact, and yet there are no first countable $L$-spaces or compact $S$-spaces. The model is one of the form $\text{PFA}\left( S \right)\left[ S \right]$, where $S$ is a coherent Souslin tree.

Keywords

54A3554D1554D2054D4503E3503E5703E65PFA(S)[S]proper forcingcoherent Souslin treelocally compactnormalcollectionwise Hausdorffsupercompact cardinal
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 64 , Issue 5 , 01 October 2012 , pp. 1182 - 1200
Copyright
Copyright © Canadian Mathematical Society 2012

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