Geodesic
Algebras of distributions for semi-isolating formulas of a complete theory
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 408-433

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We define a class of algebras describing links of binary semi-isolating formulas on the set of all realizations for a family of $1$-types of a complete theory. These algebras include algebras of isolating formulas considered before. We prove that a set of labels for binary semi-isolating formulas on the set of all realizations for a $1$-type $p$ forms a monoid of a special form with a partial order inducing ranks for labels, with set-theoretic operations, and with a composition. We describe the class of these structures. A description of the class of structures relative to families of $1$-types is given.
Keywords: type, complete theory, algebra of binary semi-isolating formulas, join of monoids, deterministic structure. 
@article{SEMR_2014_11_a12,
     author = {S. V. Sudoplatov},
     title = {Algebras of distributions for semi-isolating formulas of a complete theory},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {408--433},
     publisher = {mathdoc},
     volume = {11},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2014_11_a12/}
}
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S. V. Sudoplatov. Algebras of distributions for semi-isolating formulas of a complete theory. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 408-433. http://geodesic.mathdoc.fr/item/SEMR_2014_11_a12/