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

• Autorzy: Teruyuki Yorioka
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 54D20: Noncompact covering properties (paracompact, Lindel\"of, etc.)
• 54G20: Counterexamples
• 54A35: Consistency and independence results
• 03E35: Consistency and independence results
• 54D15: Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2008
• Tom: 201
• Numer: 1
• Strony: 53-89

Daty

wydano

2008

Twórcy

autor

Teruyuki Yorioka

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

Identyfikatory

DOI

10.4064/fm201-1-2