-bounded sets and filters on
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Keeping the covering number of the null ideal small
Teruyuki Yorioka (2015)
Fundamenta Mathematicae
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).
Killing GCH everywhere by a cofinality-preserving forcing notion over a model of GCH
Sy-David Friedman, Mohammad Golshani (2013)
Fundamenta Mathematicae
Starting from large cardinals we construct a pair V₁⊆ V₂ of models of ZFC with the same cardinals and cofinalities such that GCH holds in V₁ and fails everywhere in V₂.
Kurepa's hypothesis and the continuum
Keith Devlin (1975)
Fundamenta Mathematicae
Currently displaying 1 – 4 of 4
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