On o-Stable Expansions of

Verbovskiy V.V. Yershigeshova A.D.
December 2023 Pleiades Publishing

Lobachevskii Journal of Mathematics
2023 #44 Issue 12 5485 - 5492 pp.

Abstract: Roughly speaking, an ordered structure is o-stable if any cut in has a few extensions up to complete 1-types over. 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 has an o-stable theory.

NIP theories , o-minimal structures , o-stable theories , ordered groups

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Satbayev University, Almaty, 050013, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan
Suleyman Demirel University, Karasay region, Kaskelen, 040900, Kazakhstan

Satbayev University
Institute of Mathematics and Mathematical Modeling
Suleyman Demirel University

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