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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.23967 |
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| _version_ | 1866918471235796992 |
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| author | Boney, Will |
| author_facet | Boney, Will |
| contents | $μ$-Abstract Elementary Classes are a model theoretic framework introduced in [BGL+16] to encompass classes axiomatized by $\mathbb{L}_{\infty, \infty}$. We show that the framework extends beyond these logics by showing classes axiomatized in $\mathbb{L}(aa)$ with just the $aa$ quantifier are an $\aleph_1$-Abstract Elementary Class. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_23967 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $Σ_1$-Stationary logic as an $\aleph_1$-Abstract Elementary Class Boney, Will Logic $μ$-Abstract Elementary Classes are a model theoretic framework introduced in [BGL+16] to encompass classes axiomatized by $\mathbb{L}_{\infty, \infty}$. We show that the framework extends beyond these logics by showing classes axiomatized in $\mathbb{L}(aa)$ with just the $aa$ quantifier are an $\aleph_1$-Abstract Elementary Class. |
| title | $Σ_1$-Stationary logic as an $\aleph_1$-Abstract Elementary Class |
| topic | Logic |
| url | https://arxiv.org/abs/2410.23967 |