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

摘要

We introduce a generalization of a Dowker space constructed from a Suslintree by Mary Ellen Rudin, and the rectangle refining property for forcing notions, whichmodifies the one for partitions due to Paul B. Larson and Stevo Todorcevic and is strongerthan the countable chain condition. It is proved that Martin's Axiom for forcing no-tions with the rectangle refining property implies that every generalized Rudin spaceconstructed from Aronszajn trees is non-Dowker, and that the same can be forced with aSuslin tree. Moreover, we consider generalized Rudin spaces constructed with some typesof non-Aronszajn wi-trees under the Proper Forcing Axiom.