Geodesic
Algebras of Distributions of Binary Isolating Formulas for Quite $o$-Minimal Theories
Algebra i logika, Tome 57 (2018) no. 6, pp. 662-683

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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.
Keywords: quite o-minimal theory, countable model, convexity rank, algebras of distributions of binary isolating formulas, generalized commutative monoid. 
@article{AL_2018_57_6_a2,
     author = {D. Yu. Emel'yanov and B. Sh. Kulpeshov and S. V. Sudoplatov},
     title = {Algebras of {Distributions} of {Binary} {Isolating} {Formulas} for {Quite} $o${-Minimal} {Theories}},
     journal = {Algebra i logika},
     pages = {662--683},
     publisher = {mathdoc},
     volume = {57},
     number = {6},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2018_57_6_a2/}
}
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D. Yu. Emel'yanov; B. Sh. Kulpeshov; S. V. Sudoplatov. Algebras of Distributions of Binary Isolating Formulas for Quite $o$-Minimal Theories. Algebra i logika, Tome 57 (2018) no. 6, pp. 662-683. http://geodesic.mathdoc.fr/item/AL_2018_57_6_a2/