Abstract
Letn be a positive integer, letK n denote the theory of groups nilpotent of class at mostn, and letK + n denote the theory of torsion-free groups nilpotent of class at mostn. We show that ifn≧2 then neitherK n norK + n has a model companion. ForK n we obtain the stronger result that the class of finitely generic models is disjoint from the class of infinitely generic models. We also give some other results about existentially complete nilpotent groups.
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Dedicated to the Memory of Abraham Robinson.
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Saracino, D. Existentially complete nilpotent groups. Israel J. Math. 25, 241–248 (1976). https://doi.org/10.1007/BF02757003
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DOI: https://doi.org/10.1007/BF02757003