Viktor VerbovskiyNazym Ergozhina2026-02-172026-02-172016Viktor Verbovskiyб Nazym Ergozhina / SOME PROPERTIES OF FINITELY QUILTED ORDERED STRUCTURES / Suleyman Demirel University / СДУ ХАБАРШЫСЫ 2016. No1(36)https://repository.sdu.edu.kz/handle/123456789/2500It is knownthat any cut in an o-minimal structure has a unique extension up to a complete type over the model. For weakly o-minimal structures a cut can have at most two extensions up to complete types, and the sets of realizations of these types are convex in any elementary extensions. Generalizing weak o-minimality we obtain the following notion of an n-quilted structure: a totally ordered structure is said to be n-quilted if any cut has at most extensions up to complete types. Note that we omit here condition that the set of all realizations of a type must be convex. In this article we investigate basic properties of n-quilted structures. Since notion of o-minimality had appeared in a series of generalizations were suggested such as weak o-minimality, quasi-o-minimality, almost o-minimality, quasi weak o-minimality. C- minimality, variants of o-minimality and others.enAttribution-NonCommercial-ShareAlike 4.0 InternationalMathematical logicmodel theoryo-minimalityordered structuresa cuta complete type.Article