Every maximal ideal may be Katětov above of all 𝐹_{𝜎} ideals

Cancino-Manríquez, J.

doi:10.1090/tran/8551

Every maximal ideal may be Katětov above of all $F_\sigma$ ideals
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Abstract:

We prove that it is relatively consistent with $\mathsf {ZFC}$ that every maximal ideal is Katětov above of all $F_\sigma$ ideals. In particular, we prove that it is consistent that there is no Hausdorff ultrafilter. The main theorem answers questions from Mauro Di Nasso and Marco Forti [Proc. Amer. Math. Soc. 134 (2006), pp. 1809–1818], Jana Flašková [WDS’05 proceedings of contributed papers: part I - mathematics and computer sciences, 2005; Comment. Math. Univ. Carolin. 47 (2006), pp. 617–621; 10th Asian logic conference, World Sci. Publ., Hackensack, NJ, 2010], Osvaldo Guzmán and Michael Hrušák [Topology Appl. 259 (2019), pp. 242–250], and Mauro Di Nasso and Marco Forti [Logic and its applications, Contemp. Math., Amer. Math. Soc., Providence, RI, 2005], and gives a different model for a question from Michael Benedikt [J. Symb. Log. 63 (1998), pp. 638–662], which was originally solved by S. Shelah [Logic colloquium ’95 (Haifa), lecture notes logic, Springer, Berlin, 1998].

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