Geodesic
Algebras of distributions of binary isolating formulas for almost $\omega$-categorical weakly $o$-minimal theories
Algebra i logika, Tome 60 (2021) no. 4, pp. 369-399

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We describe distribution algebras of binary isolating formulas over $1$-type for almost $\omega$-categorical weakly $o$-minimal theories. It is proved that an isomorphism of these algebras for two $1$-types is characterized by the coincidence of binary convexity ranks, as well as by the simultaneous fulfillment of isolation, quasirationality or irrationality of the two types. A criterion is established for an algebra of formulas over a pair of not weakly orthogonal $1$-types to be generalized commutative for almost $\omega$-categorical weakly $o$-minimal theories.
Keywords: algebra of distributions of binary isolating formulas, $\omega$-categorical weakly $o$-minimal theory. 
@article{AL_2021_60_4_a0,
     author = {A. B. Altaeva and B. Sh. Kulpeshov and S. V. Sudoplatov},
     title = {Algebras of distributions of binary isolating formulas for almost $\omega$-categorical weakly $o$-minimal theories},
     journal = {Algebra i logika},
     pages = {369--399},
     publisher = {mathdoc},
     volume = {60},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2021_60_4_a0/}
}
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A. B. Altaeva; B. Sh. Kulpeshov; S. V. Sudoplatov. Algebras of distributions of binary isolating formulas for almost $\omega$-categorical weakly $o$-minimal theories. Algebra i logika, Tome 60 (2021) no. 4, pp. 369-399. http://geodesic.mathdoc.fr/item/AL_2021_60_4_a0/