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

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Yorioka T.

Fundamenta Mathematicae

2008

tom 201

nr 1

53-89

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.

Keeping the covering number of the null ideal small

100%

Yorioka T.

Fundamenta Mathematicae

2015

tom 231

nr 2

139-159

It is proved that ideal-based forcings with the side condition method of Todorcevic (1984) add no random reals. By applying Judah-Repický's preservation theorem, it is consistent with the covering number of the null ideal being ℵ₁ that there are no S-spaces, every poset of uniform density ℵ₁ adds ℵ₁ Cohen reals, there are only five cofinal types of directed posets of size ℵ₁, and so on. This extends the previous work of Zapletal (2004).

Ograniczanie wyników

2 Fundamenta Mathematicae

2 Yorioka T.

1 2015

1 2008

Wyniki wyszukiwania

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

Keeping the covering number of the null ideal small