MATHEMATICS

Non-essential expansions of weakly o-minimal theories of finite convexity rank

A. B. Altaeva^a, B. Sh. Kulpeshov^bc, S. V. Sudoplatov<sup>d

a</sup> International Information Technology University, Almaty, Kazakhstan
^b Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
^c Kazakh-British Technical University
^d Sobolev Institute of Mathematics, Novosibirsk, Russia

Abstract: We study constant expansions of weakly o-minimal theories of finite convexity rank having less than 2$^\omega$ countable models. We prove that any non-essential expansion (expansion by finitely many new constants) of a weakly o-minimal Ehrenfeucht theory of finite convexity rank preserves Ehrenfeuchtness. We also establish that the countable spectrum of such an expanded theory is not decreased.

Keywords: weak o-minimality, orthogonality of 1-types, countable model, convexity rank, Ehrenfeucht theory, non-essential expansion of a theory.

UDC: 510.67

Presented: A. L. Semenov
Received: 26.05.2025
Revised: 16.07.2025
Accepted: 19.08.2025

DOI: 10.7868/S3034504925050027

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