A characterization of strongly dependent ordered Abelian groups
Alfred Dolich, John Goodrick
TL;DR
This paper characterizes all ordered Abelian groups with a strongly dependent first-order theory in the language {+,<}, providing a comprehensive classification in model theory.
Contribution
It offers a complete characterization of strongly dependent ordered Abelian groups, a result independently obtained by Halevi-Hasson and Farré.
Findings
Complete classification of strongly dependent ordered Abelian groups
Independent confirmation of main result by Halevi-Hasson and Farré
Advances understanding of model-theoretic properties of ordered Abelian groups
Abstract
We characterize all ordered Abelian groups whose first order theory in the language {+,<} is strongly dependent. The main result of this note was obtained independently by Halevi-Hasson and Farr\'e.
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