location:  Publications → journals
Search results

Search: All articles in the CJM digital archive with keyword collectionwise Hausdorff

 Expand all        Collapse all Results 1 - 2 of 2

1. CJM Online first

Dow, Alan; Tall, Franklin D.
 Normality versus paracompactness in locally compact spaces This note provides a correct proof of the result claimed by the second author that locally compact normal spaces are collectionwise Hausdorff in certain models obtained by forcing with a coherent Souslin tree. A novel feature of the proof is the use of saturation of the non-stationary ideal on $\omega_1$, as well as of a strong form of Chang's Conjecture. Together with other improvements, this enables the consistent characterization of locally compact hereditarily paracompact spaces as those locally compact, hereditarily normal spaces that do not include a copy of $\omega_1$. Keywords:normal, paracompact, locally compact, countably tight, collectionwise Hausdorff, forcing with a coherent Souslin tree, Martin's Maximum, PFA(S)[S], Axiom R, moving off propertyCategories:54A35, 54D20, 54D45, 03E35, 03E50, 03E55, 03E57

2. CJM 2012 (vol 64 pp. 1182)

Tall, Franklin D.
 PFA$(S)[S]$: More Mutually Consistent Topological Consequences of $PFA$ and $V=L$ 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 cardinalCategories:54A35, 54D15, 54D20, 54D45, 03E35, 03E57, 03E65
 top of page | contact us | privacy | site map |