Abstract
In the paper we formulate an axiom , 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 w 1 , while 𝔠 = w 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 implies the existence of crowded and selective ultrafilters as well as nonselective P -points. In addition we prove that under every selective ultrafilter is w 1 -generated. The paper finishes with the proof that holds in the iterated perfect set model.
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