Geodesic
Algebras of distributions of binary formulas for theories of Archimedean solids
The Bulletin of Irkutsk State University. Series Mathematics, Tome 28 (2019), pp. 36-52
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Algebras of distributions of binary isolating and semi-isolating 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 semi-isolating formulas. Here the description of a finite algebra of binary isolating formulas unambiguously entails a description of the algebra of binary semi-isolating 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, flat-nosed cube, flat-nosed dodecahedron, truncated cubooctahedron, rhomboicosododecahedron, truncated icosahedron, truncated dodecahedron, rhombo-truncated icosododecahedron.
Keywords: algebra of distributions of binary formulas, Archimedean solid. 
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D. Yu. Emel'yanov. Algebras of distributions of binary formulas for theories of Archimedean solids. The Bulletin of Irkutsk State University. Series Mathematics, Tome 28 (2019), pp. 36-52. http://geodesic.mathdoc.fr/item/IIGUM_2019_28_a2/

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