Varieties generated by completions
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2018
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| _version_ | 1866912226925871104 |
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| author | Andréka, H. Németi, I. |
| author_facet | Andréka, H. Németi, I. |
| contents | We prove that persistently finite algebras are not created by completions of algebras, in any ordered discriminator variety. A persistently finite algebra is one without infinite simple extensions. We prove that finite measurable relation algebras are all persistently finite. An application of these theorems is that the variety generated by the completions of representable relation algebras does not contain all relation algebras. This answers Problem 1.1(1) from a paper by R. Maddux in the negative. At the same time, we confirm the suggestion in that paper that the finite maximal relation algebras constructed in a joint paper by M. Frias and R. Maddux are not in the variety generated by the completions of representable relation algebras. We prove that there are continuum many varieties between the variety generated by the completions of representable relation algebras and the variety of relation algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1810_04569 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Varieties generated by completions Andréka, H. Németi, I. Logic 03C05 06E25 03G15 03C13 06A06 06B23 06A11 We prove that persistently finite algebras are not created by completions of algebras, in any ordered discriminator variety. A persistently finite algebra is one without infinite simple extensions. We prove that finite measurable relation algebras are all persistently finite. An application of these theorems is that the variety generated by the completions of representable relation algebras does not contain all relation algebras. This answers Problem 1.1(1) from a paper by R. Maddux in the negative. At the same time, we confirm the suggestion in that paper that the finite maximal relation algebras constructed in a joint paper by M. Frias and R. Maddux are not in the variety generated by the completions of representable relation algebras. We prove that there are continuum many varieties between the variety generated by the completions of representable relation algebras and the variety of relation algebras. |
| title | Varieties generated by completions |
| topic | Logic 03C05 06E25 03G15 03C13 06A06 06B23 06A11 |
| url | https://arxiv.org/abs/1810.04569 |