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Extending real-valued functions in βκ

Alan Dow (1997)

Fundamenta Mathematicae

An Open Coloring Axiom type principle is formulated for uncountable cardinals and is shown to be a consequence of the Proper Forcing Axiom. Several applications are found. We also study dense C*-embedded subspaces of ω*, showing that there can be such sets of cardinality c and that it is consistent that ω*{pis C*-embedded for some but not all p ∈ ω*.

Extending the ideal of nowhere dense subsets of rationals to a P-ideal

Rafał Filipów, Nikodem Mrożek, Ireneusz Recław, Piotr Szuca (2013)

Commentationes Mathematicae Universitatis Carolinae

We show that the ideal of nowhere dense subsets of rationals cannot be extended to an analytic P-ideal, F σ ideal nor maximal P-ideal. We also consider a problem of extendability to a non-meager P-ideals (in particular, to maximal P-ideals).

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