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Search: All articles in the CJM digital archive with keyword proper forcing

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1. 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

2. CJM 2009 (vol 61 pp. 604)

Hart, Joan E.; Kunen, Kenneth
 First Countable Continua and Proper Forcing Assuming the Continuum Hypothesis, there is a compact, first countable, connected space of weight \$\aleph_1\$ with no totally disconnected perfect subsets. Each such space, however, may be destroyed by some proper forcing order which does not add reals. Keywords:connected space, Continuum Hypothesis, proper forcing, irreducible mapCategories:54D05, 03E35