This article is cited in 8 papers

Mathematical logic, algebra and number theory

Relative $e$-spectra and relative closures for families of theories

S. V. Sudoplatov<sup>abcd

a</sup> Novosibirsk State Technical University, K. Marx avenue, 20, 630073, Novosibirsk, Russia
^b Novosibirsk State University, Pirogova street, 1, 630090, Novosibirsk, Russia
^c Institute of Mathematics and Mathematical Modeling, Pushkina Street, 125, 050010, Almaty, Kazakhstan
^d Sobolev Institute of Mathematics, Academician Koptyug avenue, 4, 630090, Novosibirsk, Russia

Abstract: We define the notions of relative $e$-spectra, with respect to $E$-operators, relative closures, and relative generating sets. We study properties connected with relative $e$-spectra and relative generating sets.

Keywords: $E$-operator, combination of theories, relative $e$-spectrum, disjoint families of theories, relative closure, relative generating set.

UDC: 510.67

MSC: 03C30, 03C50, 54A05

Received January 31, 2017, published March 30, 2017

Language: English

DOI: 10.17377/semi.2017.14.027

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