Model companions for ℵ₀-categorical theories

Saracino, D.

doi:10.1090/S0002-9939-1973-0316238-1

Model companions for $\aleph _{0}$-categorical theories
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Proc. Amer. Math. Soc. 39 (1973), 591-598 Request permission

Abstract:

We show that any countable ${\aleph _0}$-categorical theory without finite models has a model companion (which is also ${\aleph _0}$-categorical). We find the model companions for all ${\aleph _0}$-categorical abelian groups, and conclude with some remarks on the ${\aleph _1}$ -categorical case.

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