Open AccessBinary convexity rank in almost omega-categorical weakly o-minimal theories
Author(s) -
Gaukhar Amirbek,
B. Sh. Kulpeshov
Publication year - 2022
Publication title -
ķazaķstan-britan tehnikalyķ universitetìnìņ habaršysy
Language(s) - English
Resource type - Journals
eISSN - 2959-8109
pISSN - 1998-6688
DOI - 10.55452/1998-6688-2022-19-1-23-29
Subject(s) - mathematics , convexity , combinatorics , intersection (aeronautics) , omega , rank (graph theory) , closure (psychology) , maximal element , categorical variable , regular polygon , type (biology) , convex set , element (criminal law) , set (abstract data type) , discrete mathematics , convex optimization , geometry , physics , statistics , aerospace engineering , ecology , computer science , financial economics , engineering , market economy , economics , biology , quantum mechanics , programming language , law , political science
The present paper concerns the notion of weak o-minimality that was initially deeply studied by D. Macpherson, D. Marker and C. Steinhorn. A subset A of a linearly ordered structure M is convex if for all a, b Î A and c Î M whenever a < c < b we have c Î A. A weakly o-minimal structure is a linearly ordered structure M = áM, =, <, …ñ such that any definable (with parameters) subset of M is a union of finitely many convex sets in M. A criterion for equality of the binary convexity ranks for non-weakly orthogonal non-algebraic 1-types in almost omega-categorical weakly o-minimal theories in case of existing an element of the set of realizations of one of these types the definable closure of which has a non-empty intersection with the set of realizations of another type is found.