Published April 24, 2023
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KATĚTOV ORDER ON MAD FAMILIES
Description
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.
Translated Descriptions
⚠️
This is an automatic machine translation with an accuracy of 90-95%
Translated Description (Arabic)
الخلاصة نواصل دراسة أمر كاتوف على العائلات المجنونة. نثبت أن الحد الأقصى للعائلات المجنونة في Katětov موجود تحت $\mathfrak {b=c }$ وأنه لا توجد عائلات مجنونة في Katětov تفترض $\mathfrak {s\leq b}.$ هذا يحسن النتائج المعروفة سابقًا من الأدبيات. نجيب أيضًا على مشكلة من Arciga و Hrušák و Martínez فيما يتعلق بأسر Katětov القصوى المجنونة.Translated Description (English)
Abstract We continue with the study of the Katětov order on MAD families. We prove that Katětov maximum 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 maximum MAD families.Translated Description (French)
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 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 Maximum MAD families.Translated Description (Spanish)
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.Files
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Additional details
Additional titles
- Translated title (Arabic)
- طلب كات. TOV للعائلات المجنونة
- Translated title (English)
- KAT. TOV ORDER ON MAD FAMILIES
- Translated title (French)
- COMMANDE DE CAT. TOV SUR MAD FAMILIES
- Translated title (Spanish)
- PEDIDO DE CATUTOV EN FAMILIAS MAD
Identifiers
- Other
- https://openalex.org/W4366778555
- DOI
- 10.1017/jsl.2023.25
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