S. V. Sudoplatov, “Approximations of theories”, Sib. Èlektron. Mat. Izv., 2020, Volume 17,Pages <nobr>715

This article is cited in 17 papers

Mathematical logic, algebra and number theory

Approximations of theories

S. V. Sudoplatov^abc

^a Sobolev Institute of Mathematics, 4, Acad. Koptyug ave., Novosibirsk, 630090, Russia
^b Novosibirsk State Technical University, 20, K. Marx ave., Novosibirsk, 630073, Russia
^c Novosibirsk State University, 1, Pirogova str., Novosibirsk, 630090, Russia

Abstract: We study approximations of theories both in general context and with respect to some natural classes of theories. Some kinds of approximations are considered, connections with finitely axiomatizable theories and minimal generating sets of theories as well as their $e$-spectra are found. $e$-categorical approximating families are introduced and characterized.

Keywords: approximation of theory, combination of structures, closure, finitely axiomatizable theory, $e$-spectrum.

UDC: 510.67

MSC: 03C30, 03C15, 03C50, 54A05

Received April 20, 2020, published May 22, 2020

DOI: 10.33048/semi.2020.17.049