Katětov order on Borel ideals

Archive for Mathematical Logic 56 (7-8):831-847 (2017)
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Abstract

We study the Katětov order on Borel ideals. We prove two structural theorems, one for Borel ideals, the other for analytic P-ideals. We isolate nine important Borel ideals and study the Katětov order among them. We also present a list of fundamental open problems concerning the Katětov order on Borel ideals.

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10.1007/s00153-017-0543-x

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Citations of this work

Ramsey type properties of ideals.M. Hrušák, D. Meza-Alcántara, E. Thümmel & C. Uzcátegui - 2017 - Annals of Pure and Applied Logic 168 (11):2022-2049.
Ways of Destruction.Barnabás Farkas & Lyubomyr Zdomskyy - 2022 - Journal of Symbolic Logic 87 (3):938-966.
On extendability to $$F_\sigma $$ ideals.Adam Kwela - 2022 - Archive for Mathematical Logic 61 (7):881-890.

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References found in this work

Analytic ideals and their applications.Sławomir Solecki - 1999 - Annals of Pure and Applied Logic 99 (1-3):51-72.
Mathias–Prikry and Laver–Prikry type forcing.Michael Hrušák & Hiroaki Minami - 2014 - Annals of Pure and Applied Logic 165 (3):880-894.
Forcing with quotients.Michael Hrušák & Jindřich Zapletal - 2008 - Archive for Mathematical Logic 47 (7-8):719-739.
Ramsey type properties of ideals.M. Hrušák, D. Meza-Alcántara, E. Thümmel & C. Uzcátegui - 2017 - Annals of Pure and Applied Logic 168 (11):2022-2049.
Forcing indestructibility of MAD families.Jörg Brendle & Shunsuke Yatabe - 2005 - Annals of Pure and Applied Logic 132 (2):271-312.

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