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

Teruyuki Yorioka. "Rudin's Dowker space in the extension with a Suslin tree." Fundamenta Mathematicae 201.1 (2008): 53-89. <http://eudml.org/doc/283328>.

@article{TeruyukiYorioka2008,
abstract = {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.},
author = {Teruyuki Yorioka},
journal = {Fundamenta Mathematicae},
keywords = {Dowker spaces; Martin's Axiom; Suslin tree; rectangle refining property},
language = {eng},
number = {1},
pages = {53-89},
title = {Rudin's Dowker space in the extension with a Suslin tree},
url = {http://eudml.org/doc/283328},
volume = {201},
year = {2008},
}

TY - JOUR
AU - Teruyuki Yorioka
TI - Rudin's Dowker space in the extension with a Suslin tree
JO - Fundamenta Mathematicae
PY - 2008
VL - 201
IS - 1
SP - 53
EP - 89
AB - 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.
LA - eng
KW - Dowker spaces; Martin's Axiom; Suslin tree; rectangle refining property
UR - http://eudml.org/doc/283328
ER -