Katětov Order on Mad Families

Journal of Symbolic Logic 89 (2):794-828 (2024)
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Abstract

We continue with the study of the Katětov order on MAD families. We prove that Katětov maximal MAD families exist under $\mathfrak {b=c}$ and that there are no Katětov-top MAD families assuming $\mathfrak {s\leq b}.$ This improves previously known results from the literature. We also answer a problem form Arciga, Hrušák, and Martínez regarding Katětov maximal MAD families.

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10.1017/jsl.2023.25

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References found in this work

Happy families.A. R. D. Mathias - 1977 - Annals of Mathematical Logic 12 (1):59.
Katětov order on Borel ideals.Michael Hrušák - 2017 - Archive for Mathematical Logic 56 (7-8):831-847.
Set Theory.Thomas Jech - 1999 - Studia Logica 63 (2):300-300.
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.
Mathias–Prikry and Laver–Prikry type forcing.Michael Hrušák & Hiroaki Minami - 2014 - Annals of Pure and Applied Logic 165 (3):880-894.

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