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arXiv · 2512.09414

Some model theory of the Heisenberg group

Maciej Frącek·Piotr Kowalski
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Abstract

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 $K$.

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Maciej Frącek, Piotr Kowalski. 2025-12-10. Some model theory of the Heisenberg group. https://arxiv.org/abs/2512.09414

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