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2 Journal of Applied Analysis

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CPAgame/prism and ultrafilters on Q and ω

Millán A.

Journal of Applied Analysis

2006

Vol. 12, nr 2

153-180

In this paper we use the version CPAgame/prism of the Covering Property Axiom, which has been formulated by Ciesielski and Paw- likowski and holds in the iterated perfect set model, to study the rela- tions between different kinds of ultrafilters on ω and Q. In particular, we will give a full account for the logical relations between the properties of being a selective ultrafilter, a P-point, a Q-point, and an ω 1-OK point.

Separately nowhere constant functions; n-cube and α-prism densities

Ciesielski K., Millán A.

Journal of Applied Analysis

2005

Vol. 11, nr 1

49-62

A function f from a countable product X= Πi Xi of Polish spaces into a Polish space is separately nowhere constant provided it is nowhere constant on every section of X. We show that every continuous separately nowhere constant function is one-to-one on a product of perfect subsets of Xi 's. This result is used to distinguish between n-cube density notions for different n ≤ ω, where ω-cube density is a basic notion behind the Covering Property Axiom CPA formulated by Ciesielski and Pawlikowski. We will also distinguish; for different values of ∝ < ω 1, between the notions of a-prism densities -the more refined density notions used also in CPA.