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

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