Abstract
In this paper, we investigate properties that are preserved or acquired when combining an arbitrary number of theories or structures. Recently, an interest has been shown in the study of P-combinations (when each structure is distinguished by a separate unary predicate) and E-combinations (when each structure is distinguished by a separate class of equivalence with respect to E). Here we studied the properties of E-combinations of linearly ordered theories. The 1-indiscernibilty and density of a weakly o-minimal E-combination of countably many copies of an almost omega-categorical weakly o-minimal theory in a language that does not contain distinguished constants are established.
Highlights
We continue the study of combinations, namely, we will consider E-combinations of almost ω-categorical weakly o-min imal theories
A weakly o-minimal structure is a linearly ordered structure such that any definable subset of the structure is the union of finitely many convex sets in
It was established that the countable spectrum might change
Summary
In [1]–[12], various combinations of theories were considered. In this paper, we continue the study of combinations, namely, we will consider E-combinations of almost ω-categorical weakly o-min imal theories.Let us introduce the necessary definitions.The notion of weak o-minimality was originally investigated by D. Мұнда сызықтық реттелген теориялардың E-комбинацияларының қасиеттерін зерттедік. Здесь мы изучали свойства Е-комбинаций линейно упорядоченных теорий. . A weakly o-minimal structure is a linearly ordered structure such that any definable (with parameters) subset of the structure is the union of finitely many convex sets in . . A countable theory is said to be almost -categorical if for any types there exist only finitely many types
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