SOME PROPERTIES OF FINITELY QUILTED ORDERED STRUCTURES

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dc.contributor.authorViktor Verbovskiy
dc.contributor.authorNazym Ergozhina
dc.contributor.authorAkbota Bektursynova
dc.date.accessioned2023-06-05T08:58:00Z
dc.date.available2023-06-05T08:58:00Z
dc.date.issued2016
dc.description.abstractIt is known that 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 n 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. It is known that 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 n 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 [1] a series of generalizations were suggested such as weak o-minimality, quasi-o-minimality, almost o-minimality, quasi weak o-minimality, Cminimality, variants of o-minimality and others.
dc.identifier.citationSOME PROPERTIES OF FINITELY QUILTED ORDERED STRUCTURES. Viktor Verbovskiy, Nazym Ergozhina, Akbota Bektursynova. Вестник СДУ - 2016
dc.identifier.urihttps://repository.sdu.edu.kz/handle/123456789/487
dc.publisherSuleyman Demirel University
dc.subjectMathematical logic
dc.subjectmodel theory
dc.subjecto-minimality
dc.subjectordered structures
dc.subjecta cut
dc.subjecta complete type
dc.subjectВестник СДУ/ СДУ хабаршысы
dc.titleSOME PROPERTIES OF FINITELY QUILTED ORDERED STRUCTURES
dc.typeArticle
dspace.entity.type

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