# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

## Extending real-valued functions in $\beta_k$

### Tom 152 / 1997

Fundamenta Mathematicae 152 (1997), 21-41 DOI: 10.4064/fm_1997_152_1_1_21_41

#### Streszczenie

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 $\mathfrak c$ and that it is consistent that ω*\{p} is C*-embedded for some but not all p ∈ ω*.

• Alan Dow

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