Some Applications of the Katětov Order on Borel Ideals

Volume 64 / 2016

Nikodem Mrożek Bulletin Polish Acad. Sci. Math. 64 (2016), 21-28 MSC: Primary 03E05; Secondary 03E15, 26A21. DOI: 10.4064/ba8055-6-2016 Published online: 11 July 2016


We construct an embedding of the algebra $\mathcal {P}(\omega )/\mathrm {Fin}$ into the family of summable ideals with the Katětov order. This construction will be used to solve two problems: about the relation between the Katětov order and the ideal Baire classes of functions, and about long chains of ideals alternately with and without the property of being a P-ideal.


  • Nikodem MrożekInstitute of Mathematics
    Faculty of Mathematics, Physics, and Informatics
    University of Gdańsk
    Wita Stwosza 57
    80-952 Gdańsk, Poland

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