This article is cited in 7 papers

Mathematical logic, algebra and number theory

On semilattices and lattices for families of theories

S. V. Sudoplatov<sup>abcd

a</sup> Sobolev Institute of Mathematics, Academician Koptyug avenue, 4, 630090, 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 Novosibirsk State Technical University, K. Marx avenue, 20, 630073, Novosibirsk, Russia

Abstract: We define and study semilattices and lattices for $E$-closed families of theories. Properties of these semilattices and lattices are investigated. It is shown that lattices for families of theories with the least generating sets are distributive.

Keywords: $E$-operator, combination of theories, family of theories, least generating set, semilattice, lattice.

UDC: 510.67

MSC: 03C30, 03C50, 54A05, 06B30

Received January 31, 2017, published September 29, 2017

Language: English

DOI: 10.17377/semi.2017.14.082

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