Splittings in varieties of logic

Fuente: arXiv
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Autores principales: Davey, Brian A., Kowalski, Tomasz, Taylor, Christopher J.
Formato: Preprint
Publicado: 2025
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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