On the downward Löwenheim-Skolem Theorem for elementary submodels
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910277671321600 |
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| author | Kunik, Matthias |
| author_facet | Kunik, Matthias |
| contents | We introduce a new definition of a model for a formal mathematical system. The definition is based upon the substitution in the formal systems, which allows a purely algebraic approach to model theory. This is very suitable for applications due to a general syntax used in the formal systems. For our models we present a new proof of the downward Löwenheim-Skolem Theorem for elementary submodels. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_03860 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the downward Löwenheim-Skolem Theorem for elementary submodels Kunik, Matthias Logic 03C07, 03F03, 03C55 We introduce a new definition of a model for a formal mathematical system. The definition is based upon the substitution in the formal systems, which allows a purely algebraic approach to model theory. This is very suitable for applications due to a general syntax used in the formal systems. For our models we present a new proof of the downward Löwenheim-Skolem Theorem for elementary submodels. |
| title | On the downward Löwenheim-Skolem Theorem for elementary submodels |
| topic | Logic 03C07, 03F03, 03C55 |
| url | https://arxiv.org/abs/2406.03860 |