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When
does $\aleph_{1}$-categoricity imply $\omega$-stability?
John T. Baldwin, Michael C. Laskowski and Saharon Shelah |
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Vol. 3 (2024), No. 3, 801–823
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DOI: 10.2140/mt.2024.3.801
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Abstract |
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For an -categorical atomic class, we clarify the space of types over the unique model of size . Using these results, we prove that if such a class has a model of size then it is -stable. |
Keywords
atomic class, categoricity, $\omega$-stable
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Mathematical Subject Classification
Primary: 03C45
Secondary: 03C48, 03C75
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Milestones
Received: 26 August 2023
Revised: 13 February 2024
Accepted: 11 March 2024
Published: 12 August 2024
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Authors |
| John T. Baldwin | |
| University of Illinois at
Chicago Chicago, IL United States |
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| Michael C. Laskowski | |
| University of Maryland College Park, MD United States |
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| Saharon Shelah | |
| Hebrew University of Jerusalem Jerusalem Israel |
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| © 2024 MSP (Mathematical Sciences Publishers). |
