Geodesic
Algebras of binary formulas for $\aleph_0$-categorical weakly circularly minimal theories: piecewise monotonic case
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 824-832.

Voir la notice de l'article provenant de la source Math-Net.Ru

Algebras of binary isolating formulas are described for $\aleph_0$-categorical $1$-transitive non-primitive weakly circularly minimal theories of convexity rank greater than $1$ having a non-trivial piecewise (non-strictly) monotonic function.
Keywords: weak circular minimality, algebra of binary formulas, $\aleph_0$-categorical theory, circularly ordered structure, convexity rank. 
@article{SEMR_2023_20_2_a6,
     author = {B. Sh. Kulpeshov},
     title = {Algebras of binary formulas for $\aleph_0$-categorical weakly circularly minimal theories: piecewise monotonic case},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {824--832},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a6/}
}
TY  - JOUR
AU  - B. Sh. Kulpeshov
TI  - Algebras of binary formulas for $\aleph_0$-categorical weakly circularly minimal theories: piecewise monotonic case
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2023
SP  - 824
EP  - 832
VL  - 20
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a6/
LA  - en
ID  - SEMR_2023_20_2_a6
ER  - 
%0 Journal Article
%A B. Sh. Kulpeshov
%T Algebras of binary formulas for $\aleph_0$-categorical weakly circularly minimal theories: piecewise monotonic case
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2023
%P 824-832
%V 20
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a6/
%G en
%F SEMR_2023_20_2_a6
B. Sh. Kulpeshov. Algebras of binary formulas for $\aleph_0$-categorical weakly circularly minimal theories: piecewise monotonic case. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 824-832. http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a6/

[1] S.V. Sudoplatov, Classification of countable models of complete theories, Novosibirsk, NSTU, 2018

[2] I.V. Shulepov, S.V. Sudoplatov, “Algebras of distributions for isolating formulas of a complete theory”, Sib. Èlectron. Math. Izv., 11 (2014), 380–407 | MR | Zbl

[3] S.V. Sudoplatov, “Algebras of distributions for semi-isolating formulas of a complete theory”, Sib. Èlektron. Mat. Izv., 11 (2014), 408–433 | MR | Zbl

[4] D.Yu. Emel'yanov, B.Sh. Kulpeshov, S.V. Sudoplatov, “Algebras of distributions for binary formulas in countably categorical weakly o-minimal structures”, Algerba Logic, 56:1 (2017), 13–36 | DOI | MR | Zbl

[5] K.A. Baikalova, D.Yu. Emel'yanov, B.Sh. Kulpeshov, E.A. Palyutin, S.V. Sudoplatov, “On algebras of distributions of binary isolating formulas for theories of abelian groups and their ordered enrichments”, Russ. Math., 62:4 (2018), 1–12 | DOI | MR | Zbl

[6] D.Yu. Emel'yanov, B.Sh. Kulpeshov, S.V. Sudoplatov, “Algebras of distributions of binary isolating formulas for quite o-minimal theories”, Algebra Logic, 57:6 (2019), 429–444 | DOI | MR | Zbl

[7] A.B. Altayeva, B.Sh. Kulpeshov, S.V. Sudoplatov, “Algebras of distributions of binary isolating formulas for almost $\omega$-categorical weakly o-minimal theories”, Algebra Logic, 60:4 (2021), 241–262 | DOI | MR | Zbl

[8] B.Sh. Kulpeshov, H.D. Macpherson, “Minimality conditions on circularly ordered structures”, Math. Log. Q., 51:4 (2005), 377–399 | DOI | MR | Zbl

[9] D. Macpherson, C. Steinhorn, “On variants of o-minimality”, Ann. Pure Appl. Logic, 79:2 (1996), 165–209 | DOI | MR | Zbl

[10] B.Sh. Kulpeshov, “On $\aleph_0$-categorical weakly circularly minimal structures”, Math. Log. Q., 52:6 (2006), 555–574 | DOI | MR | Zbl

[11] B.Sh. Kulpeshov, “Definable functions in the $\aleph_0$-categorical weakly circularly minimal structures”, Sib. Math. J., 50:2 (2009), 282–301 | DOI | MR | Zbl

[12] B.Sh. Kulpeshov, “On indiscernibility of a set in circularly ordered structures”, Sib. Èlektron. Mat. Izv., 12 (2015), 255–266 | DOI | MR | Zbl

[13] B.Sh. Kulpeshov, V.V. Verbovskiy, “On weakly circularly minimal groups”, Math. Log. Q., 61:1-2 (2015), 82–90 | DOI | MR | Zbl

[14] B.Sh. Kulpeshov, A.B. Altayeva, “Binary formulas in countably categorical weakly circularly minimal structures”, Algebra Logic, 55:3 (2016), 226–241 | DOI | MR | Zbl

[15] B.Sh. Kulpeshov, “On almost binarity in weakly circularly minimal structures”, Eurasian Math. J., 7:2 (2016), 38–49 | MR | Zbl

[16] A.B. Altayeva, B.Sh. Kulpeshov, “Almost binarity of countably categorical weakly circularly minimal structures”, Math. Notes, 110:6 (2021), 813–829 | DOI | MR | Zbl

[17] B.Sh. Kulpeshov, “Weakly o-minimal structures and some of their properties”, J. Symb. Log., 63:4 (1998), 1511–1528 | DOI | MR | Zbl

[18] B.Sh. Kulpeshov, “A criterion for binarity of almost $\omega$-categorical weakly o-minimal theories”, Sib. Math. J., 62:6 (2021), 1063–1075 | DOI | MR | Zbl

[19] D.Yu. Emel'yanov, B.Sh. Kulpeshov, S.V. Sudoplatov, “Algebras of binary formulas for compositions of theories”, Algebra Logic, 59:4 (2020), 295–312 | DOI | MR | Zbl

[20] B.Sh. Kulpeshov, S.V. Sudoplatov, “Algebras of binary formulas for weakly circularly minimal theories with non-trivial definable closure”, Lobachevskii J. Math., 43:12 (2022), 3532–3540 | DOI | MR | Zbl