Ehrenfeucht-Fraïssé Games for Continuous First-Order Logic
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909181104095232 |
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| author | Hirvonen, Åsa Puljujärvi, Joni |
| author_facet | Hirvonen, Åsa Puljujärvi, Joni |
| contents | We define a version of the Ehrenfeucht-Fraïssé game in the setting of metric model theory and continuous first-order logic and show that the second player having a winning strategy in a game of length $n$ exactly corresponds to being elementarily equivalent up to quantifier rank $n$. We then demonstrate the usefulness of the game with some examples. Finally, we discus connections between the game of length $ω$ and infinitary logic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_16662 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ehrenfeucht-Fraïssé Games for Continuous First-Order Logic Hirvonen, Åsa Puljujärvi, Joni Logic 03C66, 03C75 We define a version of the Ehrenfeucht-Fraïssé game in the setting of metric model theory and continuous first-order logic and show that the second player having a winning strategy in a game of length $n$ exactly corresponds to being elementarily equivalent up to quantifier rank $n$. We then demonstrate the usefulness of the game with some examples. Finally, we discus connections between the game of length $ω$ and infinitary logic. |
| title | Ehrenfeucht-Fraïssé Games for Continuous First-Order Logic |
| topic | Logic 03C66, 03C75 |
| url | https://arxiv.org/abs/2402.16662 |