Decidable varieties of p-algebras
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929499681062912 |
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| author | Kowalski, Tomasz Słomczyńska, Katarzyna |
| author_facet | Kowalski, Tomasz Słomczyńska, Katarzyna |
| contents | We show that for quasivarieties of p-algebras the properties of (i) having decidable first-order theory and (ii) having decidable first-order theory of the finite members, coincide. The only two quasivarieties with these properties are the trivial variety and the variety of Boolean algebras. This contrasts sharply, even for varieties, with the situation in Heyting algebras where decidable varieties do not coincide with finitely decidable ones. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09015 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Decidable varieties of p-algebras Kowalski, Tomasz Słomczyńska, Katarzyna Logic 03G10 (Primary) 06D15, 03B25 (Secondary) We show that for quasivarieties of p-algebras the properties of (i) having decidable first-order theory and (ii) having decidable first-order theory of the finite members, coincide. The only two quasivarieties with these properties are the trivial variety and the variety of Boolean algebras. This contrasts sharply, even for varieties, with the situation in Heyting algebras where decidable varieties do not coincide with finitely decidable ones. |
| title | Decidable varieties of p-algebras |
| topic | Logic 03G10 (Primary) 06D15, 03B25 (Secondary) |
| url | https://arxiv.org/abs/2409.09015 |