Ivanova contact join-semilattices are not finitely axiomatizable
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915209849864192 |
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| author | Lipparini, Paolo |
| author_facet | Lipparini, Paolo |
| contents | We show that the class of Contact join-semilattices, as introduced by T. Ivanova, is not finitely axiomatizable. On the other hand, a simple finite axiomatization exists for the class of those join semilattices with a weak contact relation which can be embedded into the reduct of a Boolean algebra (equivalently, a distributive lattice) with a weak contact relation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_12599 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Ivanova contact join-semilattices are not finitely axiomatizable Lipparini, Paolo Logic Rings and Algebras 03G25, 06A12, 06F99, 54E05 We show that the class of Contact join-semilattices, as introduced by T. Ivanova, is not finitely axiomatizable. On the other hand, a simple finite axiomatization exists for the class of those join semilattices with a weak contact relation which can be embedded into the reduct of a Boolean algebra (equivalently, a distributive lattice) with a weak contact relation. |
| title | Ivanova contact join-semilattices are not finitely axiomatizable |
| topic | Logic Rings and Algebras 03G25, 06A12, 06F99, 54E05 |
| url | https://arxiv.org/abs/2311.12599 |