Reduced powers of -trees
Keith Devlin (1983)
Fundamenta Mathematicae
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Keith Devlin (1983)
Fundamenta Mathematicae
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Teruyuki Yorioka (2008)
Fundamenta Mathematicae
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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...
Keith Devlin (1972)
Fundamenta Mathematicae
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Kurepa, Đuro (1985)
Publications de l'Institut Mathématique. Nouvelle Série
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I. Juhász, William Weiss (1978)
Fundamenta Mathematicae
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Lajos Soukup (1990)
Commentationes Mathematicae Universitatis Carolinae
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Ronald Jensen, Håvard Johnsbråten (1974)
Fundamenta Mathematicae
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Akira Iwasa, Peter J. Nyikos (2006)
Commentationes Mathematicae Universitatis Carolinae
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It is independent of the usual (ZFC) axioms of set theory whether every collectionwise Hausdorff tree is either metrizable or has an uncountable chain. We show that even if we add “or has an Aronszajn subtree,” the statement remains ZFC-independent. This is done by constructing a tree as in the title, using the set-theoretic hypothesis , which holds in Gödel’s Constructible Universe.