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

Tall, Franklin D.

Canadian journal of mathematics, Tome 64 (2012) no. 5, pp. 1182-1200

Résumé

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.

Détail

DOI : 10.4153/CJM-2012-010-0

Mots-clés : 54A35, 54D15, 54D20, 54D45, 03E35, 03E57, 03E65, PFA(S)[S], proper forcing, coherent Souslin tree, locally compact, normal, collectionwise Hausdorff, supercompact cardinal

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