TY - JOUR

T1 - Algebras of Distributions of Binary Isolating Formulas for Quite o-Minimal Theories

AU - Emel’yanov, D. Yu

AU - Kulpeshov, B. Sh

AU - Sudoplatov, S. V.

PY - 2019/1/15

Y1 - 2019/1/15

N2 - Algebras of distributions of binary isolating formulas over a type for quite o-minimal theories with nonmaximal number of countable models are described. It is proved that an isomorphism of these algebras for two 1-types is characterized by the coincidence of convexity ranks and also by simultaneous satisfaction of isolation, quasirationality, or irrationality of those types. It is shown that for quite o-minimal theories with nonmaximum many countable models, every algebra of distributions of binary isolating formulas over a pair of nonweakly orthogonal types is a generalized commutative monoid.

AB - Algebras of distributions of binary isolating formulas over a type for quite o-minimal theories with nonmaximal number of countable models are described. It is proved that an isomorphism of these algebras for two 1-types is characterized by the coincidence of convexity ranks and also by simultaneous satisfaction of isolation, quasirationality, or irrationality of those types. It is shown that for quite o-minimal theories with nonmaximum many countable models, every algebra of distributions of binary isolating formulas over a pair of nonweakly orthogonal types is a generalized commutative monoid.

KW - algebras of distributions of binary isolating formulas

KW - convexity rank

KW - countable model

KW - generalized commutative monoid

KW - quite o-minimal theory

UR - http://www.scopus.com/inward/record.url?scp=85063813692&partnerID=8YFLogxK

U2 - 10.1007/s10469-019-09515-5

DO - 10.1007/s10469-019-09515-5

M3 - Article

AN - SCOPUS:85063813692

VL - 57

SP - 429

EP - 444

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

IS - 6

ER -