Nonvaluational ordered Abelian groups of finite burden

Masato Fujita

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arXiv · 2502.18721

Nonvaluational ordered Abelian groups of finite burden

Masato Fujita

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Abstract

Consider an expansion $\mathcal R=(R,<,+,\ldots)$ of an ordered divisible Abelian group of finite burden defining no nonempty subset $X$ of $R$ which is dense and codense in a definable open subset $U$ of $R$ with $X \subseteq U$. We further assume that $\mathcal R$ is nonvaluational, that is, for every nonempty definable subsets $A,B$ of $R$ with $A <B$ and $A \cup B=R$, $\inf\{b-a\;|\;a \in A, b \in B\}=0$. Then, $\mathcal R$ is $*$-locally weakly o-minimal. We also give a complete description of sets definable in a definably complete expansion of ordered group of burden two if it defines an infinite discrete set.

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BibTeX RIS

Masato Fujita. 2025-02-26. Nonvaluational ordered Abelian groups of finite burden. https://arxiv.org/abs/2502.18721

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