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

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 $$F_\sigma $$Fσ ideals. In this paper we discuss these orders on analytic P-ideals and Borel ideals. We prove the following:The family of all analytic P-ideals has the largest element with respect to the Katětov and the Katětov–Blass orders.The family of all Borel ideals is countably upward directed with respect to the Katětov and the Katětov–Blass orders. In the course of the proof of the latter result, we also prove that for any analytic ideal $$\mathcal {I}$$I there is a Borel ideal $$\mathcal {J}$$J with $$\mathcal {I} \subseteq \mathcal {J}$$I⊆J.