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Ideals over ω and cardinal invariants of the continuum

Published online by Cambridge University Press:  12 March 2014

P. Matet  and
J. Pawlikowski
P. Matet
Affiliation:
Mathematiques, Universite de Caen, 14032 Caen Cedex, France E-mail: [email protected]
J. Pawlikowski
Affiliation:
Instytut Matematyczny, Uniwersytet Wrocławski, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland E-mail: [email protected]
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Abstract

Let P be any one of the following combinatorial properties: weak P-pointness, weak (semi-) Q-pointness, weak (semi-)selectivity, ω-closedness. We deal with the following two questions: (1) What is the least cardinal k such that there exists an ideal with k many generators that does not have the property P? (2) Can one extend every ideal with the property P to a prime ideal with the property P?

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 63 , Issue 3 , September 1998 , pp. 1040 - 1054
Copyright
Copyright © Association for Symbolic Logic 1998

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