Published October 3, 2022
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PARTITION FORCING AND INDEPENDENT FAMILIES
- 1. University of Vienna
Description
Abstract We show that Miller partition forcing preserves selective independent families and P -points, which implies the consistency of $\mbox {cof}(\mathcal {N})=\mathfrak {a}=\mathfrak {u}=\mathfrak {i}<\mathfrak {a}_T=\omega _2$ . In addition, we show that Shelah's poset for destroying the maximality of a given maximal ideal preserves tight mad families and so we establish the consistency of $\mbox {cof}(\mathcal {N})=\mathfrak {a}=\mathfrak {i}=\omega _1<\mathfrak {u}=\mathfrak {a}_T=\omega _2$ .
Translated Descriptions
⚠️
This is an automatic machine translation with an accuracy of 90-95%
Translated Description (Arabic)
الخلاصة نوضح أن فرض تقسيم ميلر يحافظ على عائلات مستقلة انتقائية ونقاط P، مما يعني اتساق $\mbox {cof}(\mathcal {N})=\mathfrak {a}=\mathfrak {u}=\mathfrak {i}<\mathfrak {a}_T=\omega _2$ . بالإضافة إلى ذلك، نظهر أن موقف شيلا لتدمير الحد الأقصى لمثال أقصى معين يحافظ على العائلات المجنونة الضيقة وبالتالي نؤسس اتساق $\mbox {cof}(\mathcal {N})=\mathfrak {a}=\mathfrak {i}=\omega _1<\mathfrak {u}=\mathfrak {a}_T=\omega _2$ .Translated Description (English)
Abstract We show that Miller partition forcing preserves selective independent families and P -points, which implies the consistency of $\mbox {cof}(\mathcal {N})=\mathfrak {a}=\mathfrak {u}=\mathfrak {i}<\mathfrak {a}_T=\omega _2$ . In addition, we show that Shelah's poset for destroying the maximality of a given maximal ideal preserves tight mad families and so we establish the consistency of $\mbox {cof}(\mathcal {N})=\mathfrak {a}=\mathfrak {i}=\omega _1<\mathfrak {u}=\mathfrak {a}_T=\omega _2$ .Translated Description (French)
Abstract We show that Miller partition forcing preserves selective independent families and P -points, which implies the consistency of $ \mbox {cof}(\mathcal {N})=\mathfrak {a}=\mathfrak {u}=\mathfrak {i}<\mathfrak {a}_T=\omega _2 $ . In addition, we show that Shelah' s poset for destroying the maximity of a given maximal ideal preserves tight mad families and so we establish the consistency of $ \mbox {cof}(\mathcal {N})=\mathfrak {a}=\mathfrak {i}=\omega _1<\mathfrak {u}=\mathfrak {a}_T=\omega _2 $ .Translated Description (Spanish)
Abstract We show that Miller partition forcing preserves selective independent families and P -points, which implies the consistency of $\mbox {cof}(\mathcal {N})=\mathfrak {a}=\mathfrak {u}=\mathfrak {i}<\mathfrak {a}_T=\omega _2$ . In addition, we show that Shelah 's poset for destroying the maximality of a given maximal ideal preserves tight mad families and so we establish the consistency of $\mbox {cof}(\mathcal {N})=\mathfrak {a}=\mathfrak {i}=\omega _1<\mathfrak {u}=\mathfrak {a}_T=\omega _2$ .Files
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Additional details
Additional titles
- Translated title (Arabic)
- إجبار التقسيم والأسر المستقلة
- Translated title (English)
- PARTITION FORCING AND INDEPENDENT FAMILIES
- Translated title (French)
- PARTITION FORCING AND INDEPENDENT FAMILIES
- Translated title (Spanish)
- PARTITION FORCING AND INDEPENDENT FAMILIES
Identifiers
- Other
- https://openalex.org/W4300961449
- DOI
- 10.1017/jsl.2022.68
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