Geodesic
Positivеly prime models over a normal basic set
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 4 (2007), pp. 596-604 
E. A. Palyutin. Positivеly prime models over a normal basic set. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 4 (2007), pp. 596-604. http://geodesic.mathdoc.fr/item/SEMR_2007_4_a31/
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Voir la notice de l'article provenant de la source Math-Net.Ru

For given universal domain $C$, a set $\mathrm{BF}$ of normal formulas, and $A\subseteq C$, we construct substructures $B$ of $C$ with the following properties: (a) $A\subseteq B$; (b) for each $a\in B$ the type ${\rm tp}(a;(B\setminus\{a\}))$ is based by formulas from $\mathrm{BF}$. The existence and uniqueness theorems are proven. This is a generalization of the known results on the injective hulls in the variety of the modules in case when the theory $\mathrm{Th}(C^\omega)$ is stable.

[1] S. Shelah, Classification theory and the number of non-isomorphic models, North-Holland, Amsterdam, 1978 | MR | Zbl

[2] E. A. Palyutin, “Kategorichnye khornovy klassy. 1”, Algebra i logika, 19:5 (1980), 582–614 | MR | Zbl

[3] E. A. Palyutin, “Primitivno svyaznye teorii”, Algebra i logika, 39:2 (2000), 145–169 | MR | Zbl