Publications de l'Institut Mathematique 2015 Volume 97, Issue 111, Pages: 33-41
https://doi.org/10.2298/PIM140318001I
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Groups with finitely many countable models

Ilić Dejan (Faculty of Transport and Traffic Engineering, Belgrade)
Moconja Slavko (Faculty of Mathematics, Belgrade)
Tanović Predrag (Mathematical Institute SANU, Belgrade + Faculty of Mathematics, Belgrade)

We construct Abelian group with an extra structure whose first order theory has finitely many but more than one countable model.