Geodesic
Algebras of binary formulas for compositions of theories
Algebra i logika, Tome 59 (2020) no. 4, pp. 432-457

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We consider algebras of binary formulas for compositions of theories both in the general case and as applied to $\aleph_0$-categorical, strongly minimal, and stable theories, linear preorders, cyclic preorders, and series of finite structures. It is shown that $e$-definable compositions preserve isomorphisms and elementary equivalence and have basicity formed by basic formulas of the initial theories. We find criteria for $e$-definable compositions to preserve $\aleph_0$-categoricity, strong minimality, and stability. It is stated that $e$-definable compositions of theories specify compositions of algebras of binary formulas. A description of forms of these algebras is given relative to compositions with linear orders, cyclic orders, and series of finite structures.
Keywords: algebra of binary formulas, composition of theories, $\aleph_0$-categorical theory, strongly minimal theory, stable theory, linear preorder, cyclic preorder.
Mots-clés : $e$-definable composition 
@article{AL_2020_59_4_a1,
     author = {D. Yu. Emelyanov and B. Sh. Kulpeshov and S. V. Sudoplatov},
     title = {Algebras of binary formulas for compositions of theories},
     journal = {Algebra i logika},
     pages = {432--457},
     publisher = {mathdoc},
     volume = {59},
     number = {4},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2020_59_4_a1/}
}
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D. Yu. Emelyanov; B. Sh. Kulpeshov; S. V. Sudoplatov. Algebras of binary formulas for compositions of theories. Algebra i logika, Tome 59 (2020) no. 4, pp. 432-457. http://geodesic.mathdoc.fr/item/AL_2020_59_4_a1/