Splittings in varieties of logic
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866911155112378368 |
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| author | Davey, Brian A. Kowalski, Tomasz Taylor, Christopher J. |
| author_facet | Davey, Brian A. Kowalski, Tomasz Taylor, Christopher J. |
| contents | We study splittings, or lack of them, in lattices of subvarieties of some logic-related varieties. We present a general lemma, the Non-Splitting Lemma, which when combined with some variety-specific constructions, yields each of our negative results: the variety of commutative integral residuated lattices contains no splittings algebras, and in the varieties of double Heyting algebras, dually pseudocomplemented Heyting algebras and regular double p-algebras the only splitting algebras are the two-element and three-element chains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_11623 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Splittings in varieties of logic Davey, Brian A. Kowalski, Tomasz Taylor, Christopher J. Logic 08B15 (Primary) 03G10, 06F99 (Secondary) We study splittings, or lack of them, in lattices of subvarieties of some logic-related varieties. We present a general lemma, the Non-Splitting Lemma, which when combined with some variety-specific constructions, yields each of our negative results: the variety of commutative integral residuated lattices contains no splittings algebras, and in the varieties of double Heyting algebras, dually pseudocomplemented Heyting algebras and regular double p-algebras the only splitting algebras are the two-element and three-element chains. |
| title | Splittings in varieties of logic |
| topic | Logic 08B15 (Primary) 03G10, 06F99 (Secondary) |
| url | https://arxiv.org/abs/2509.11623 |