## Tsukuba Journal of Mathematics

### Structural properties of ideals over $\mathscr P_{\kappa}\lambda$ I

Yoshihiro Abe

#### 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.

#### Article information

Source
Tsukuba J. Math., Volume 39, Number 1 (2015), 83-95.

Dates
First available in Project Euclid: 7 August 2015

https://projecteuclid.org/euclid.tkbjm/1438951818

Digital Object Identifier
doi:10.21099/tkbjm/1438951818

Mathematical Reviews number (MathSciNet)
MR3383879

Zentralblatt MATH identifier
1337.03069

#### Citation

Abe, Yoshihiro. Structural properties of ideals over $\mathscr P_{\kappa}\lambda$ I. Tsukuba J. Math. 39 (2015), no. 1, 83--95. doi:10.21099/tkbjm/1438951818. https://projecteuclid.org/euclid.tkbjm/1438951818