Some model theory of the Heisenberg group
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910016140738560 |
|---|---|
| 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 |