Crowded and Selective Ultrafilters under the Covering Property Axiom
نویسنده
چکیده
In the paper we formulate an axiom CPA 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 ω1, while c = ω2: the independence number i, the reaping number r, the almost disjoint number a, and the ultrafilter base number u. We will also show that CPA prism implies the existence of crowded and selective ultrafilters as well as nonselective P -points. In addition we prove that under CPA prism every selective ultrafilter is ω1-generated. The paper finishes with the proof that CPA prism holds in the iterated perfect set model.
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