Geodesic
Algebras of distributions for isolating formulas of a complete theory
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 380-407

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We define a class of algebras describing links of binary isolating formulas on a set of realizations for a family of $1$-types of a complete theory. We prove that a set of labels for binary isolating formulas on a set of realizations for a $1$-type $p$ forms a groupoid of a special form if there is an atomic model over a realization of $p$. We describe the class of these groupoids and consider features of these groupoids in a general case and for special theories. A description of the class of partial groupoids relative to families of $1$-types is given.
Keywords: type, complete theory, groupoid of binary isolating formulas, deterministic structure.
Mots-clés : join of groupoids 
@article{SEMR_2014_11_a11,
     author = {I. V. Shulepov and S. V. Sudoplatov},
     title = {Algebras of distributions for isolating formulas of a complete theory},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {380--407},
     publisher = {mathdoc},
     volume = {11},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2014_11_a11/}
}
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I. V. Shulepov; S. V. Sudoplatov. Algebras of distributions for isolating formulas of a complete theory. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 380-407. http://geodesic.mathdoc.fr/item/SEMR_2014_11_a11/