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Crowded and Selective Ultrafilters under the Covering Property Axiom
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K. Ciesielski
Published/Copyright:
June 9, 2010
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 w1, while 𝔠 = w2: 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 w1-generated. The paper finishes with the proof that holds in the iterated perfect set model.
Key words and phrases.: Ultrafilter; selective; crowded; P-point; rational numbers; independence; reaping; almost disjoint; covering
Received: 2002-05-17
Revised: 2002-12-11
Published Online: 2010-06-09
Published in Print: 2003-June
© Heldermann Verlag
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Keywords for this article
Ultrafilter;
selective;
crowded;
P-point;
rational numbers;
independence;
reaping;
almost disjoint;
covering
Articles in the same Issue
- Skew Products of Ideals
- Crowded and Selective Ultrafilters under the Covering Property Axiom
- Solution of the Stieltjes Truncated Moment Problem
- Minimax Solutions of the Dual Hamilton-Jacobi Equation
- Nonexistence of Global Solutions to a Class of Nonlinear Differential Inequalities and Application to Hyperbolic–Elliptic Problems
- Functions of Two Variables Whose Vertical Sections Are Equiderivatives
- On Maximal Element Problem and Quasi-Variational Inequality Problem in L.C. Metric Spaces
- On a Certain Generalization of the Krasnosel'skii Theorem
