Abstract
Roughly speaking, an ordered structure \((M,<,\dots)\) is o-stable if any cut in \(M\) has a few extensions up to complete 1-types over \(M\). A theory is o-stable if all its models are. O-stability is a generalization of (weak) o-minimality and quasi-o-minimality by using the notion of a stable theory. In the paper, we prove that no proper (essential) expansion of the ordered group of integers \((\mathbb{Z},<,+)\) has an o-stable theory.
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The authors were supported by the grant BR20281002 of the SC of the MSHE of the Republic of Kazakhstan.
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Verbovskiy, V.V., Yershigeshova, A.D. On o-Stable Expansions of \(\boldsymbol{(\mathbb{Z},<,+)}\). Lobachevskii J Math 44, 5485–5492 (2023). https://doi.org/10.1134/S1995080223120387
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DOI: https://doi.org/10.1134/S1995080223120387