Abstract
AbstractWe introduce the relation of almost‐reduction in an arbitrary topological Ramsey space ℛ as a generalization of the relation of almost‐inclusion on ℕ[∞]. This leads us to a type of ultrafilter 𝒰 ⊆ ℛ which corresponds to the well‐known notion of selective ultrafilter on ℕ. The relationship turns out to be rather exact in the sense that it permits us to lift several well‐known facts about selective ultrafilters on ℕ and the Ellentuck space ℕ[∞] to the ultrafilter 𝒰 and the Ramsey space ℛ. For example, we prove that the open coloring axiom holds on L (ℝ)[𝒰], extending therefore the result from [3] which gives the same conclusion for the Ramsey space ℕ[∞]. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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