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July 2015 Structural properties of ideals over $\mathscr P_{\kappa}\lambda$ I
Yoshihiro Abe
Tsukuba J. Math. 39(1): 83-95 (July 2015). DOI: 10.21099/tkbjm/1438951818

Abstract

We try to take a first step to a theory of the structural properties of ideals over $\mathscr P_{\kappa}\lambda$, that was studied in detail by Baumgartner, Taylor and Wagon [1] for $\kappa$;. In defining the basic notions, P-points, Q-points, and selective ideals, we put importance on the behavior of the function on $\mathscr P_{\kappa}\lambda$ to the bounded ideal and Rudin-Keisler ordering.

Several facts hold similarly as on $\kappa$;, for instance, the bounded ideal is a nowhere Q-point. However some differences exist such as the bounded ideal is isomorphic to another ideal. We state the sufficient condition for ideals to be Q-points and the weakly normal ideals selective.

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Yoshihiro Abe. "Structural properties of ideals over $\mathscr P_{\kappa}\lambda$ I." Tsukuba J. Math. 39 (1) 83 - 95, July 2015. https://doi.org/10.21099/tkbjm/1438951818

Information

Published: July 2015
First available in Project Euclid: 7 August 2015

zbMATH: 1337.03069
MathSciNet: MR3383879
Digital Object Identifier: 10.21099/tkbjm/1438951818

Subjects:
Primary: 03E35 , 03E55

Keywords: $\mathscr $\mathscr P_{\kappa}\lambda$ , bounded ideal , structural property , weak normality

Rights: Copyright © 2015 University of Tsukuba, Institute of Mathematics

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Vol.39 • No. 1 • July 2015
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