
The Bulletin of Irkutsk State University. Series Mathematics, 2019, Volume 28, Pages 36–52
(Mi iigum371)




Algebras of distributions of binary formulas for theories of Archimedean solids
D. Yu. Emel'yanov^{} ^{} Novosibirsk State Technical University, Novosibirsk, Russian Federation
Abstract:
Algebras of distributions of binary isolating and semiisolating formulas are derived objects for given theory and reflect binary formula relations between realizations of $1$types. These algebras are associated with the following natural classification questions: 1) for a given class of theories, determine which algebras correspond to the theories from this class and classify these algebras; 2) to classify theories from a given class depending on the algebras defined by these theories of isolating and semiisolating formulas. Here the description of a finite algebra of binary isolating formulas unambiguously entails a description of the algebra of binary semiisolating formulas, which makes it possible to track the behavior of all binary formula relations of a given theory.
In the article we describe algebras of binary formulas for the theories of Archimedean solids. For the obtained algebras, Cayley tables are given. It is shown that these algebras are exhausted by described algebras for a truncated cube, truncated octahedron, rhombocuboctahedron, icosododecahedron, truncated tetrahedron, cubooctahedron, flatnosed cube, flatnosed dodecahedron, truncated cubooctahedron, rhomboicosododecahedron, truncated icosahedron, truncated dodecahedron, rhombotruncated icosododecahedron.
Keywords:
algebra of distributions of binary formulas, Archimedean solid.
DOI:
https://doi.org/10.26516/19977670.2019.28.36
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Bibliographic databases:
UDC:
510.67:514.146
MSC: 03C07, 03C60, 03G15, 51E30 Received: 25.04.2019
Citation:
D. Yu. Emel'yanov, “Algebras of distributions of binary formulas for theories of Archimedean solids”, The Bulletin of Irkutsk State University. Series Mathematics, 28 (2019), 36–52
Citation in format AMSBIB
\Bibitem{Eme19}
\by D.~Yu.~Emel'yanov
\paper Algebras of distributions of binary formulas for theories of Archimedean solids
\jour The Bulletin of Irkutsk State University. Series Mathematics
\yr 2019
\vol 28
\pages 3652
\mathnet{http://mi.mathnet.ru/iigum371}
\crossref{https://doi.org/10.26516/19977670.2019.28.36}
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