Algebras of Distributions of Binary Isolating Formulas for Quite o-Minimal Theories
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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.
Keywordsquite o-minimal theory countable model convexity rank algebras of distributions of binary isolating formulas generalized commutative monoid
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