On Katětov and Katětov–Blass orders on analytic P-ideals and Borel ideals

Abstract

Minami–Sakai (Arch Math Logic 55(7–8):883–898, 2016) investigated the cofinal types of the Katětov and the Katětov–Blass orders on the family of all $$F_\sigma $$ ideals. In this paper we discuss these orders on analytic P-ideals and Borel ideals. We prove the following: In the course of the proof of the latter result, we also prove that for any analytic ideal $$\mathcal {I}$$ there is a Borel ideal $$\mathcal {J}$$ with $$\mathcal {I} \subseteq \mathcal {J}$$ .