B. Sh. Kulpeshov, S. V. Sudoplatov, “On freedom and independence in hypergraphs of models of theories”, Sib. Èlektron. Mat. Izv., 2018, Volume 15,Pages <nobr>612

Mathematical logic, algebra and number theory

On freedom and independence in hypergraphs of models of theories

B. Sh. Kulpeshov^a, S. V. Sudoplatov^bcd

^a International Information Technologies University, Manas str. 34A/Zhandosov str. 8A, 050040, Almaty, Kazakhstan
^b Novosibirsk State University, Pirogova street, 1, 630090, Novosibirsk, Russia
^c Sobolev Institute of Mathematics, Academician Koptyug avenue, 4, 630090, Novosibirsk, Russia
^d Novosibirsk State Technical University, K. Marx avenue, 20, 630073, Novosibirsk, Russia

Abstract: The notions of freedom and independence for hypergraphs of models of a theory are introduced. We study properties of these notions in general case and for some natural classes of theories. We describe hypergraphs of models for theories of unary predicates, equivalence relations and study the properties of hypergraphs for ordered theories and for theories of unars.

Keywords: hypergraph of models, elementary theory, free set, independent sets, complete union of hypergraphs.

UDC: 510.67

MSC: 03C07, 03C50, 03C64, 54A05

Received March 3, 2018, published May 24, 2018

Language: English

DOI: 10.17377/semi.2018.15.049