Dp-minimal expansions of discrete ordered abelian groups

Erik Walsberg

Dp-minimal expansions of discrete ordered abelian groups

Logic 2020-04-29 v2

Authors: Erik Walsberg

Abstract

If $\mathcal{Z}$ is a dp-minimal expansion of a discrete ordered abelian group $(Z,<,+)$ and $\mathcal{Z}$ does not admit a nontrivial definable convex subgroup then $\mathcal{Z}$ is interdefinable with $(Z,<,+)$ and $(Z,<,+)$ is elementarily equivalent to $(\mathbb{Z},<,+)$ .

Keywords

dp-minimal discrete ordered abelian groups definable convex subgroup interdefinable elementary equivalence

Cite

@article{arxiv.1903.06222,
  title  = {Dp-minimal expansions of discrete ordered abelian groups},
  author = {Erik Walsberg},
  journal= {arXiv preprint arXiv:1903.06222},
  year   = {2020}
}

Comments

This has be superseded by arXiv:1909.05399

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