An NIP-like Notion in Abstract Elementary Classes
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914115499327488 |
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| author | Yang, Wentao |
| author_facet | Yang, Wentao |
| contents | This paper is a contribution to "neo-stability" type of result for abstract elementary classes. Under certain set theoretic assumptions, we propose a definition and a characterization of NIP in AECs. The class of AECs with NIP properly contains the class of stable AECs. We show that for an AEC $K$ and $λ\geq LS(K)$, $K_λ$ is NIP if and only if there is a notion of nonforking on it which we call a w*-good frame. On the other hand, the negation of NIP leads to being able to encode subsets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_04125 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An NIP-like Notion in Abstract Elementary Classes Yang, Wentao Logic Primary: 03C45, 03C48. Secondary: 03C52 This paper is a contribution to "neo-stability" type of result for abstract elementary classes. Under certain set theoretic assumptions, we propose a definition and a characterization of NIP in AECs. The class of AECs with NIP properly contains the class of stable AECs. We show that for an AEC $K$ and $λ\geq LS(K)$, $K_λ$ is NIP if and only if there is a notion of nonforking on it which we call a w*-good frame. On the other hand, the negation of NIP leads to being able to encode subsets. |
| title | An NIP-like Notion in Abstract Elementary Classes |
| topic | Logic Primary: 03C45, 03C48. Secondary: 03C52 |
| url | https://arxiv.org/abs/2303.04125 |