Displaying similar documents to “Preserving P-points in definable forcing”

On iterated forcing for successors of regular cardinals

Todd Eisworth (2003)

Fundamenta Mathematicae

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We investigate the problem of when ≤λ-support iterations of < λ-complete notions of forcing preserve λ⁺. We isolate a property- properness over diamonds-that implies λ⁺ is preserved and show that this property is preserved by λ-support iterations. Our condition is a relative of that presented by Rosłanowski and Shelah in [2]; it is not clear if the two conditions are equivalent. We close with an application of our technology by presenting a consistency result on uniformizing colorings...

The Wholeness Axioms and the Class of Supercompact Cardinals

Arthur W. Apter (2012)

Bulletin of the Polish Academy of Sciences. Mathematics

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We show that certain relatively consistent structural properties of the class of supercompact cardinals are also relatively consistent with the Wholeness Axioms.

Hybrid Prikry forcing

Dima Sinapova (2015)

Fundamenta Mathematicae

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We present a new forcing notion combining diagonal supercompact Prikry forcing with interleaved extender based forcing. We start with a supercompact cardinal κ. In the final model the cofinality of κ is ω, the singular cardinal hypothesis fails at κ, and GCH holds below κ. Moreover we define a scale at κ which has a stationary set of bad points in the ground model.

Indestructibility, strongness, and level by level equivalence

Arthur W. Apter (2003)

Fundamenta Mathematicae

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We construct a model in which there is a strong cardinal κ whose strongness is indestructible under κ-strategically closed forcing and in which level by level equivalence between strong compactness and supercompactness holds non-trivially.

Inaccessible cardinals without the axiom of choice

Andreas Blass, Ioanna M. Dimitriou, Benedikt Löwe (2007)

Fundamenta Mathematicae

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We consider four notions of strong inaccessibility that are equivalent in ZFC and show that they are not equivalent in ZF.