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PFA$(S)[S]$: More Mutually Consistent Topological Consequences of $PFA$ and $V=L$ |
Canad. J. Math. 64(2012), 1182-1200
Published:2012-06-26
Printed: Oct 2012
Printed: Oct 2012
- Franklin D. Tall,
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 |