KATĚTOV ORDER ON MAD FAMILIES

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 proble...

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Bibliographic Details
Published in:The Journal of symbolic logic 2024-06, Vol.89 (2), p.794-828
Main Author: GUZMÁN, OSVALDO
Format: Article
Language:English
Subjects:
Logic
Mathematics
Symbolism
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Summary: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.
ISSN:0022-4812
1943-5886
DOI:10.1017/jsl.2023.25