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This article is cited in 1 scientific paper (total in 1 paper)
On deterministic and absorbing algebras of binary formulas of polygonometrical theories
D. Yu. Emelyanova, S. V. Sudoplatovabcd a Novosibirsk State University, 1, Pirogov st., Novosibirsk, 630090
b Novosibirsk State Technical University, 20, K. Marx av., Novosibirsk, 630073
c Sobolev Institute of Mathematics SB RAS, 4, Academician Koptyug Avenue, Novosibirsk, 630090
d Institute of Mathematics and Mathematical Modeling, 125, Pushkina st., Almaty, Kazakhstan, 050010
Abstract:
Algebras of distributions of binary isolating and semi-isolating formulas
are derived structures for a given theory. These algebras reflect
binary links between realizations of $1$-types defined by
formulas of the initial theory. Thus these are two sorts of
interrelated classification problems: 1) to define, for a given
class of theories, what algebras correspond to theories in this
class and to classify these algebras; 2) to classify theories in
the class in the dependence of algebras of isolating and
semi-isolating algebras that defined by these theories. For the
finite algebras of binary isolating formulas that description
implies the description for the algebra of binary semi-isolating
formulas.
In the paper, we investigate deterministic, almost deterministic,
and absorbing algebras of binary formulas of polygonometrical
theories.
The properties of determinism and almost determinism for algebras
of binary isolating formulas of polygonometrical theories are
characterized. As corollary we have that any group generates a
deterministic algebra of a polygonometrical theory. The notion of
$n$-almost deterministic algebra is introduced, examples and
properties of these algebras are stated. A description of these
algebras for theories of graphs of regular polyhedrons is given.
It is shown that any group is a side-group of a trigonometry with
$2$-absorbing algebra of binary isolating formulas.
Keywords:
algebra of binary formulas, deterministic algebra, absorbing algebra, polygonometrical theory.
Citation:
D. Yu. Emelyanov, S. V. Sudoplatov, “On deterministic and absorbing algebras of binary formulas of polygonometrical theories”, Bulletin of Irkutsk State University. Series Mathematics, 20 (2017), 32–44
Linking options:
https://www.mathnet.ru/eng/iigum303 https://www.mathnet.ru/eng/iigum/v20/p32
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