Geodesic
Properties of existentially closed companions
Algebra i logika, Tome 57 (2018) no. 3, pp. 321-337

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Necessary and sufficient conditions are stated for an arbitrary theory to be an elementary theory for a class of its existentially closed models. Conditions are given under which some existentially closed model simultaneously realizes one maximal existential type and omits another. We also prove a theorem on a prime existentially closed model over a maximal existential type. Considerable complexity of existentially closed structures and their theories was noted by A. Macintyre. Therefore, the examples of existentially closed companions having any finite or countable number of pairwise non elementarily equivalent existentially closed models constructed here are of interest.
Keywords: elementary theory, existentially closed model, existentially closed companion, existential type. 
@article{AL_2018_57_3_a4,
     author = {A. T. Nurtazin},
     title = {Properties of existentially closed companions},
     journal = {Algebra i logika},
     pages = {321--337},
     publisher = {mathdoc},
     volume = {57},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2018_57_3_a4/}
}
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A. T. Nurtazin. Properties of existentially closed companions. Algebra i logika, Tome 57 (2018) no. 3, pp. 321-337. http://geodesic.mathdoc.fr/item/AL_2018_57_3_a4/