Crowded and selective ultrafilters under the covering property axiom

Ciesielski, K.; Pawlikowski, J.

Artykuł - szczegóły

Tytuł artykułu

Crowded and selective ultrafilters under the covering property axiom

Autorzy

Ciesielski K. , Pawlikowski J.

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Warianty tytułu

Języki publikacji

Abstrakty

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.

Słowa kluczowe

ultrafilter selective crowded P-point rational numbers independence reaping almost disjoint covering

ultrafiltr wybiorczy zatłoczony P-punkt liczby wymierne niezależność czerpanie prawie rozłączne pokrycie

Wydawca

De Gruyter

Czasopismo

Journal of Applied Analysis

Rocznik

2003

Tom

Vol. 9, nr 1

Strony

19--55

Opis fizyczny

Bibliogr. 27 poz.

Twórcy

autor

Ciesielski K.

k_cies@math.wvu.edu

Department of Mathematics, West Virginia University, Morgantown, WV 26506-6310 USA

autor

Pawlikowski J.

pawlikow@math.uni.wroc.pl

Department of Mathematics, University of Wroclaw, pl. Grunwaldzki 2/4, 50-384 Wroclaw, Poland

Bibliografia

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