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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2512.09414 |
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| _version_ | 1866910016140738560 |
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| author | Frącek, Maciej Kowalski, Piotr |
| author_facet | Frącek, Maciej Kowalski, Piotr |
| contents | We show that a field $K$ is model complete (in the language of rings) if and only if the Heisenberg group $H(K)$ is model complete (in the language of groups). To show that, we extend Levchuk's result about automorphisms of $H(K)$ to the case of monomorphisms $H(K)\to H(M)$. We also show that $H(K)$ does not have quantifier elimination and discuss its (non-)bi-interpretability with $K$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_09414 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some model theory of the Heisenberg group Frącek, Maciej Kowalski, Piotr Logic We show that a field $K$ is model complete (in the language of rings) if and only if the Heisenberg group $H(K)$ is model complete (in the language of groups). To show that, we extend Levchuk's result about automorphisms of $H(K)$ to the case of monomorphisms $H(K)\to H(M)$. We also show that $H(K)$ does not have quantifier elimination and discuss its (non-)bi-interpretability with $K$. |
| title | Some model theory of the Heisenberg group |
| topic | Logic |
| url | https://arxiv.org/abs/2512.09414 |