Algebras of distributions of binary isolating formulas for quite o-minimal theories. (English. Russian original) Zbl 1468.03049
Algebra Logic 57, No. 6, 429-444 (2019); translation from Algebra Logika 57, No. 6, 662-683 (2018).
Summary: 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.
MSC:
| 03C64 | Model theory of ordered structures; o-minimality |
| 03C15 | Model theory of denumerable and separable structures |
| 03C07 | Basic properties of first-order languages and structures |
Keywords:
quite o-minimal theory; countable model; convexity rank; algebras of distributions of binary isolating formulas; generalized commutative monoidReferences:
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