Browsing by Author "Viktor Verbovskiy"

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    SOME PROPERTIES OF FINITELY QUILTED ORDERED STRUCTURES
    (Suleyman Demirel University, 2016) Viktor Verbovskiy; Nazym Ergozhina; Akbota Bektursynova
    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. 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.