Model-theoretic Tameness in finite extensions of groups

Yatir Halevi; Saharon Shelah

Model-theoretic Tameness in finite extensions of groups

Logic 2026-05-15 v1 Group Theory

Authors: Yatir Halevi , Saharon Shelah

Abstract

It is shown that finite-index extensions and finite-index subgroups of $\omega$ -stable groups can be model-theoretically wild. More precisely, there exists an $\omega$ -stable group $G$ such that any given countable first-order structure in a finite language is interpretable both in some finite-index extension of $G$ and in some finite-index subgroup of $G$ .

Keywords

model-theoretic tameness omega-stable groups finite-index extensions finite-index subgroups first-order structure

Cite

@article{arxiv.2605.14390,
  title  = {Model-theoretic Tameness in finite extensions of groups},
  author = {Yatir Halevi and Saharon Shelah},
  journal= {arXiv preprint arXiv:2605.14390},
  year   = {2026}
}

Model-theoretic Tameness in finite extensions of groups

Abstract

Keywords

Cite

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