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 ω₁-trees under the Proper Forcing Axiom.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm201-1-2,
author = {Teruyuki Yorioka},
title = {Rudin's Dowker space in the extension with a Suslin tree},
journal = {Fundamenta Mathematicae},
volume = {201},
year = {2008},
pages = {53-89},
zbl = {1165.03038},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm201-1-2}
}
Teruyuki Yorioka. Rudin's Dowker space in the extension with a Suslin tree. Fundamenta Mathematicae, Tome 201 (2008) pp. 53-89. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm201-1-2/