In the paper we formulate an axiom CPA_{prism}^{game},
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 \omega_{1}, while \continuum=\omega_{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
CPA_{prism}^{game} implies the existence of
crowded and selective ultrafilters as well as nonselective P-points.
In addition we prove that under CPA_{prism}^{game}
every selective ultrafilter is \omega_{1}-generated. The paper is
finished with the proof that CPA_{prism}^{game}
holds in the iterated perfect set model.

It is known that the axiom CPA_{prism}^{game} captures the essence of the Sacks model concerning standard cardinal characteristics of continuum. This follows from a resent result of J. Zapletal who proved, assuming large cardinals, that for a ``nice'' cardinal invariant \kappa if \kappa<\continuum holds in any forcing extension than \kappa<\continuum follows already from CPA_{prism}^{game}.

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**Last modified August 27, 2003.**