location:  Publications → journals → CJM
Abstract view

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

Published:2012-06-26
Printed: Oct 2012
• Franklin D. Tall,
Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4
Features coming soon:
Citations   (via CrossRef) Tools: Search Google Scholar:
 Format: LaTeX MathJax PDF

## Abstract

Extending the work of Larson and Todorcevic, we show 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 PFA$(S)[S]$, where $S$ is a coherent Souslin tree.
 Keywords: PFA$(S)[S]$, proper forcing, coherent Souslin tree, locally compact, normal, collectionwise Hausdorff, supercompact cardinal
 MSC Classifications: 54A35 - Consistency and independence results [See also 03E35] 54D15 - Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.) 54D20 - Noncompact covering properties (paracompact, Lindelof, etc.) 54D45 - Local compactness, $\sigma$-compactness 03E35 - Consistency and independence results 03E57 - Generic absoluteness and forcing axioms [See also 03E50] 03E65 - Other hypotheses and axioms