Geodesic
Arities and aritizabilities of first-order theories
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 2, pp. 889-901.

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

We study and describe possibilities for arities of elementary theories and of their expansions. Links for arities with respect to Boolean algebras, to disjoint unions and to compositions of structures are shown. Arities and aritizabilities are semantically characterized. The dynamics for arities of theories is described. Possibilities for arities and aritizabilities of theories are illustrated by a series of natural geometric, combinatorial and model-theoretic examples.
Keywords: elementary theory, arity, expansion, aritizability. 
@article{SEMR_2022_19_2_a12,
     author = {S. V. Sudoplatov},
     title = {Arities and aritizabilities of first-order theories},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {889--901},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2022_19_2_a12/}
}
TY  - JOUR
AU  - S. V. Sudoplatov
TI  - Arities and aritizabilities of first-order theories
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2022
SP  - 889
EP  - 901
VL  - 19
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2022_19_2_a12/
LA  - en
ID  - SEMR_2022_19_2_a12
ER  - 
%0 Journal Article
%A S. V. Sudoplatov
%T Arities and aritizabilities of first-order theories
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2022
%P 889-901
%V 19
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2022_19_2_a12/
%G en
%F SEMR_2022_19_2_a12
S. V. Sudoplatov. Arities and aritizabilities of first-order theories. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 2, pp. 889-901. http://geodesic.mathdoc.fr/item/SEMR_2022_19_2_a12/

[1] S.V. Sudoplatov, “On a certain complexity estimate in graph theory”, Sib. Math. J., 37:3 (1996), 614–671 | DOI | MR | Zbl

[2] S.V. Sudoplatov, “Transitive arrangements of algebraic systems”, Sib. Math. J., 40:6 (1999), 1142–1145 | DOI | MR | Zbl

[3] A.I. Maltsev, Algebraic systems, Springer-Verlag, Berlin etc, 1973 | MR | Zbl

[4] L. Henkin, J.D. Monk, A. Tarski, Cylindric algebras, v. 1, North-Holland Publishing Company, Amsterdam-London, 1971 | MR | Zbl

[5] L. Henkin, J.D. Monk, A. Tarski, I. Nemeti, Cylindric set algebras. Cylindric set algebras and related structures, Lecture Notes in Mathematics, 883, Springer-Verlag, Berlin etc., 1981 | DOI | MR | Zbl

[6] L. Henkin, J.D. Monk, A. Tarski, Cylindric algebras, v. II, Studies in Logic and the Foundations of Mathematics, 115, North-Holland, Amsterdam etc., 1985 | MR | Zbl

[7] T. Imieliński, Jr.W. Lipski, “The relational model of data and cylindric algebras”, J. Comput. Syst. Sci., 28:1 (1984), 80–102 | 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] B.S. Baizhanov, B.Sh. Kulpeshov, “On behaviour of 2-formulas in weakly o-minimal theories”, Mathematical Logic in Asia, Proceedings of the 9th Asian Logic Conference, eds. Goncharov S. S. (ed.) et al., World Scientific, Hackensack, 2006, 31–40 | DOI | MR | Zbl

[10] B.Sh. Kulpeshov, “Criterion for binarity of $\aleph_0$-categorical weakly o-minimal theories”, Ann. Pure Appl. Logic, 145:3 (2007), 354–367 | DOI | MR | Zbl

[11] A.B. Altaeva, B.Sh. Kulpeshov, “On almost binary weakly circularly minimal structures”, Bulletin of Karaganda University, Mathematics, 78:2 (2015), 74–82 | MR

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

[13] A.B. Altaeva, B.Sh. Kulpeshov, “Binarity of almost $\omega$-categorical quite o-minimal theories”, Sib. Math. J., 61:3 (2020), 379–390 | DOI | MR | Zbl

[14] 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

[15] A.L. Semenov, “Finiteness conditions for algebras of relations”, Proc. Steklov Inst. Math., 242 (2003), 92–96 | MR | Zbl

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

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

[18] B.Sh. Kulpeshov, S.V. Sudoplatov, “On algebras of distributions of binary formulas for quite $o$-minimal theories”, News of the National Academy of Sciences of the Republic of Kazakhstan. Physical-Mathematical Series, 300:2 (2015)

[19] D.Yu. Emel'yanov, “On algebras of distributions of binary formulas for theories of unars”, Izv. Irkutsk. Gos. Univ., Ser. Mat., 17 (2016), 23–36 | Zbl

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

[21] D.Yu. Emel'yanov, S.V. Sudoplatov, “On deterministic and absorbing algebras of binary formulas of polygonometrical theories”, Izv. Irkutsk. Gos. Univ., Ser. Mat., 20 (2017), 32–44 | MR | Zbl

[22] 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

[23] D.Yu. Emel'yanov, B.Sh. Kulpeshov, S.V. Sudoplatov, “On algebras of distributions for binary formulas for quite o-minimal theories”, Algebra Logic, 57:6 (2018), 429–444 | DOI | MR | Zbl

[24] 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

[25] E.A. Palyutin, J. Saffe, S.S. Starchenko, “Models of superstable Horn theories”, Algebra Logic, 24:3 (1985), 171–210 | DOI | MR | Zbl

[26] S.V. Sudoplatov, “Syntactic approach to constructions of generic models”, Algebra Logic, 46:2 (2007), 134–146 | DOI | MR | Zbl

[27] S.V. Sudoplatov, Basedness of stable theories and properties of countable models with powerful types, Dis. cand. fiz.-mat. sc. 01.01.06, Novosibirsk, 1990

[28] S. Shelah, Classification theory and the number of non-isomorphic models, North-Holland, Amsterdam etc, 1990 | MR | Zbl

[29] V. Harnik, L. Harrington, “Fundamentals of forking”, Ann. Pure Appl. Logic, 26:3 (1984), 245–286 | DOI | MR | Zbl

[30] R.E. Woodrow, Theories with a finite number of countable models and a small language, Ph. D. Thesis, Simon Fraser University, 1976 | MR

[31] J.T. Baldwin, A. Lachlan, “On strongly minimal sets”, J. Symb. Log., 36:1 (1971), 79–96 | DOI | MR | Zbl