Representability for distributive quasi relation algebras via nested sums
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914306981888000 |
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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 |