Elementary extensions of almost o-minimal structures

Mourad Berraho; Akito Tsuboi

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arXiv · 2602.04286

Elementary extensions of almost o-minimal structures

Mourad Berraho·Akito Tsuboi

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Abstract

This paper investigates almost o-minimal structures, a weakening of o-minimality introduced by Fujita to capture structures that lie outside the classical o-minimal framework. In contrast to o-minimality and local o-minimality, almost o-minimality is not preserved under elementary equivalence. This raises the natural question of whether every almost o-minimal structure admits a proper elementary extension that is again almost o-minimal. The main result of this paper provides an affirmative answer to this question.

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BibTeX RIS

Mourad Berraho, Akito Tsuboi. 2026-02-04. Elementary extensions of almost o-minimal structures. https://arxiv.org/abs/2602.04286

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