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PFA(S)[S]: More Mutually Consistent Topological Consequences of PFA and V = L
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- Journal:
- Canadian Journal of Mathematics / Volume 64 / Issue 5 / 01 October 2012
- Published online by Cambridge University Press:
- 20 November 2018, pp. 1182-1200
- Print publication:
- 01 October 2012
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- Article
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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.
