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1 Journal of Applied Analysis

1 2003

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Crowded and selective ultrafilters under the covering property axiom

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Ciesielski K. , Pawlikowski J.

Journal of Applied Analysis

2003

tom Vol. 9, nr 1

19-55

In the paper we formulate an axiom CPAgame prism, which is the most prominent version of the Covering Property Axiom CPA, and discuss several of its implications. In particular, we show that it implies that the following cardinal characteristics of continuum are equal to ω 1 , while c = ω 2 : the independence number i, the reaping number r, the almost disjoint number a, and the ultrafilter base number u. We will also show that CPAgame prism, implies the existence of crowded and selective ultrafilters as well as nonselective P-points. In addition we prove that under CPAgame prism every selective ultrafilter is ω 1-generated. The paper finishes with the proof that CPAgame prism holds in the iterated perfect set model.