This article is cited in 1 paper

Mathematical logic, algebra and number theory

On axiomatizability of the class of finitary matroids and decidability of their universal theory

A. V. Il'ev^a, V. P. Il'ev<sup>b

a</sup> Sobolev Institute of Mathematics, 13, Pevtsova str., Omsk, 644043, Russia
^b Dostoevsky Omsk State University, 55a, Mira ave., Omsk, 644077, Russia

Abstract: 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.

UDC: 510.67, 519.151

MSC: 03C48, 05B35

Received February 17, 2020, published October 26, 2020

DOI: 10.33048/semi.2020.17.118

Bibliographic databases:

•