A strong failure of ℵ 0 -stability for atomic classes
We study classes of atomic models AtT of a countable, complete first-order theory T. We prove that if AtT is not pcl-small, i.e., there is an atomic model N that realizes uncountably many types over pclN(a¯) for some finite a¯ from N, then there are 2ℵ1 non-isomorphic atomic models of T, each of siz...
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| Veröffentlicht in: | Archive for mathematical logic 2019-01, Vol.58 (1), p.99-118 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
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| Online-Zugang: | Volltext |
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| Zusammenfassung: | We study classes of atomic models AtT of a countable, complete first-order theory T. We prove that if AtT is not pcl-small, i.e., there is an atomic model N that realizes uncountably many types over pclN(a¯) for some finite a¯ from N, then there are 2ℵ1 non-isomorphic atomic models of T, each of size ℵ1. |
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| ISSN: | 0933-5846 1432-0665 |
| DOI: | 10.1007/s00153-018-0623-6 |