Twist-structures isomorphic to modal Nelson lattices
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916685377699840 |
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| author | Menchón, Paula Rodriguez, Ricardo O. |
| author_facet | Menchón, Paula Rodriguez, Ricardo O. |
| contents | In this paper, we introduce a new variety of Heyting algebras with two unary modal operators that are not interdefinable but satisfy the weakest condition necessary to define modal operators on Nelson lattices. To achieve this, we utilize the representation of Nelson lattices as twist structures over Heyting algebras and establish a categorical equivalence. Finally, we develop a topological duality for this new variety and apply it to derive a topological duality for modal Nelson lattices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_08109 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Twist-structures isomorphic to modal Nelson lattices Menchón, Paula Rodriguez, Ricardo O. Logic In this paper, we introduce a new variety of Heyting algebras with two unary modal operators that are not interdefinable but satisfy the weakest condition necessary to define modal operators on Nelson lattices. To achieve this, we utilize the representation of Nelson lattices as twist structures over Heyting algebras and establish a categorical equivalence. Finally, we develop a topological duality for this new variety and apply it to derive a topological duality for modal Nelson lattices. |
| title | Twist-structures isomorphic to modal Nelson lattices |
| topic | Logic |
| url | https://arxiv.org/abs/2504.08109 |