On Some Infinitary Logics
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866929250209103872 |
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| author | Vaananen, Jouko Velickovic, Boban |
| author_facet | Vaananen, Jouko Velickovic, Boban |
| contents | We define a new class of infinitary logics $\mathscr L^1_{κ,α}$ generalizing Shelah's logic $\mathbb L^1_κ$ defined in \cite{MR2869022}. If $κ=\beth_κ$ and $α<κ$ is infinite then our logic coincides with $\mathbb L^1_κ$. We study the relation between these logics for different parameters $κ$ and $α$. We give many examples of classes of structures that can or cannot be defined in these logics. Finally, we give a different version of Lindström's Theorem for $\mathbb L^1_κ$ in terms of the $ϕ$-submodel relation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_13344 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Some Infinitary Logics Vaananen, Jouko Velickovic, Boban Logic Primary: 03Bxx, 03C55, 03C75, 03C95, 03Exx We define a new class of infinitary logics $\mathscr L^1_{κ,α}$ generalizing Shelah's logic $\mathbb L^1_κ$ defined in \cite{MR2869022}. If $κ=\beth_κ$ and $α<κ$ is infinite then our logic coincides with $\mathbb L^1_κ$. We study the relation between these logics for different parameters $κ$ and $α$. We give many examples of classes of structures that can or cannot be defined in these logics. Finally, we give a different version of Lindström's Theorem for $\mathbb L^1_κ$ in terms of the $ϕ$-submodel relation. |
| title | On Some Infinitary Logics |
| topic | Logic Primary: 03Bxx, 03C55, 03C75, 03C95, 03Exx |
| url | https://arxiv.org/abs/2402.13344 |