Geodesic
Existentially closed and maximal models in positive logic
Algebra i logika, Tome 51 (2012) no. 6, pp. 748-765

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It is proved that a subclass of positively existentially closed models of any finitely axiomatizable $h$-universal class in a predicate signature is axiomatizable. We construct examples suggesting the necessity of these conditions for the given subclass to be axiomatizable. The concept of an $h$-maximal model is introduced. It is shown that a subclass of $h$-maximal models of any finitely axiomatizable $h$-universal class is also finitely axiomatizable. Moreover, the set of positively existentially closed models in an $h$-universally axiomatizable class coincides with the set of positively existentially closed models in its subclass of $h$-maximal models.
Keywords: finitely axiomatizable $h$-universal class, positively existentially closed model. 
@article{AL_2012_51_6_a3,
     author = {A. Kungozhin},
     title = {Existentially closed and maximal models in positive logic},
     journal = {Algebra i logika},
     pages = {748--765},
     publisher = {mathdoc},
     volume = {51},
     number = {6},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2012_51_6_a3/}
}
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A. Kungozhin. Existentially closed and maximal models in positive logic. Algebra i logika, Tome 51 (2012) no. 6, pp. 748-765. http://geodesic.mathdoc.fr/item/AL_2012_51_6_a3/