Rudin's Dowker space in the extension with a Suslin tree

Teruyuki Yorioka¹

¹ Department of Mathematics Shizuoka University Ohya 836, Shizuoka, 422-8529, Japan

Fundamenta Mathematicae, Tome 201 (2008) no. 1, pp. 53-89.

Résumé

We introduce a generalization of a Dowker space constructed from a Suslin tree by Mary Ellen Rudin, and the rectangle refining property for forcing notions, which modifies the one for partitions due to Paul B. Larson and Stevo Todorčević and is stronger than the countable chain condition. It is proved that Martin's Axiom for forcing notions with the rectangle refining property implies that every generalized Rudin space constructed from Aronszajn trees is non-Dowker, and that the same can be forced with a Suslin tree. Moreover, we consider generalized Rudin spaces constructed with some types of non-Aronszajn $\omega _1$-trees under the Proper Forcing Axiom.

Détail

DOI : 10.4064/fm201-1-2

Keywords: introduce generalization dowker space constructed suslin tree mary ellen rudin rectangle refining property forcing notions which modifies partitions due paul larson stevo todor evi stronger countable chain condition proved martins axiom forcing notions rectangle refining property implies every generalized rudin space constructed aronszajn trees non dowker forced suslin tree moreover consider generalized rudin spaces constructed types non aronszajn omega trees under proper forcing axiom