Equational theories of idempotent semifields
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929617484382208 |
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| author | Metcalfe, George Santschi, Simon |
| author_facet | Metcalfe, George Santschi, Simon |
| contents | This paper provides answers to several open problems about equational theories of idempotent semifields. In particular, it is proved that (i) no equational theory of a non-trivial class of idempotent semifields has a finite basis; (ii) there are continuum-many equational theories of classes of idempotent semifields; and (iii) the equational theory of the class of idempotent semifields is co-NP-complete. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_09876 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Equational theories of idempotent semifields Metcalfe, George Santschi, Simon Logic 12K10, 16Y60, 03C05, 06F15 This paper provides answers to several open problems about equational theories of idempotent semifields. In particular, it is proved that (i) no equational theory of a non-trivial class of idempotent semifields has a finite basis; (ii) there are continuum-many equational theories of classes of idempotent semifields; and (iii) the equational theory of the class of idempotent semifields is co-NP-complete. |
| title | Equational theories of idempotent semifields |
| topic | Logic 12K10, 16Y60, 03C05, 06F15 |
| url | https://arxiv.org/abs/2402.09876 |