Representability for distributive quasi relation algebras via nested sums

Fuente: arXiv
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Autores principales: Craig, Andrew, Robinson, Claudette, Morton, Wilmari
Formato: Preprint
Publicado: 2025
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author Craig, Andrew
Robinson, Claudette
Morton, Wilmari
author_facet Craig, Andrew
Robinson, Claudette
Morton, Wilmari
contents We extend the work of Galatos (2004) on nested sums, originally called generalised ordinal sums, of residuated lattices. We show that the nested sum of an odd quasi relation algebra (qRA) satisfying certain conditions and an arbitrary qRA is again a qRA. In a recent paper by Craig and Robinson (2025) the notion of representability for distributive quasi relation algebras (DqRAs) was developed. For certain pairs of representable DqRAs, we prove that their nested sum is again representable. An important consequence of this result is that finite Sugihara chains are finitely representable.
format Preprint
id arxiv_https___arxiv_org_abs_2503_06657
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Representability for distributive quasi relation algebras via nested sums
Craig, Andrew
Robinson, Claudette
Morton, Wilmari
Logic
Rings and Algebras
06F05, 03B47, 03G10
We extend the work of Galatos (2004) on nested sums, originally called generalised ordinal sums, of residuated lattices. We show that the nested sum of an odd quasi relation algebra (qRA) satisfying certain conditions and an arbitrary qRA is again a qRA. In a recent paper by Craig and Robinson (2025) the notion of representability for distributive quasi relation algebras (DqRAs) was developed. For certain pairs of representable DqRAs, we prove that their nested sum is again representable. An important consequence of this result is that finite Sugihara chains are finitely representable.
title Representability for distributive quasi relation algebras via nested sums
topic Logic
Rings and Algebras
06F05, 03B47, 03G10
url https://arxiv.org/abs/2503.06657