Geodesic
On axiomatizability of the class of finitary matroids and decidability of their universal theory
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 1730-1740 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In the paper, finitary matroids are studied by means of the model theory. It is shown that the class of finitary matroids is nonaxiomatizable. Decidability of the universal theory of this class is proved.
Keywords: axiomatizability, finitary matroid, universal theory, decidability. 
@article{SEMR_2020_17_a39,
     author = {A. V. Il'ev and V. P. Il'ev},
     title = {On axiomatizability of the class of finitary matroids and decidability of their universal theory},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1730--1740},
     year = {2020},
     volume = {17},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2020_17_a39/}
}
TY  - JOUR
AU  - A. V. Il'ev
AU  - V. P. Il'ev
TI  - On axiomatizability of the class of finitary matroids and decidability of their universal theory
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2020
SP  - 1730
EP  - 1740
VL  - 17
UR  - http://geodesic.mathdoc.fr/item/SEMR_2020_17_a39/
LA  - ru
ID  - SEMR_2020_17_a39
ER  - 
%0 Journal Article
%A A. V. Il'ev
%A V. P. Il'ev
%T On axiomatizability of the class of finitary matroids and decidability of their universal theory
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2020
%P 1730-1740
%V 17
%U http://geodesic.mathdoc.fr/item/SEMR_2020_17_a39/
%G ru
%F SEMR_2020_17_a39
A. V. Il'ev; V. P. Il'ev. On axiomatizability of the class of finitary matroids and decidability of their universal theory. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 1730-1740. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a39/

[1] M. Aigner, Combinatorial Theory, Mir, M., 1982 | MR

[2] Yu.L. Ershov, E.A. Palyutin, Mathematical logic, Nauka, M., 1987 | MR | Zbl

[3] A.V. Il'ev, “On axiomatizability of hereditary classes of graphs and matroids”, Sib. Electron. Math. Izv., 13 (2016), 137–147 | MR | Zbl

[4] A.V. Il'ev, V.P. Il'ev, “On axiomatizability and decidability of universal theories of hereditary classes of matroids”, Journal of Physics: Conference Series, 1210 (2019), 012056 | DOI

[5] H. Whitney, “On the abstract properties of linear dependence”, Am. J. Math., 57 (1935), 509–533 | DOI | MR | Zbl