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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Model companions for $ \aleph \sb{0}$-categorical theories


Author: D. Saracino
Journal: Proc. Amer. Math. Soc. 39 (1973), 591-598
MSC: Primary 02H05
DOI: https://doi.org/10.1090/S0002-9939-1973-0316238-1
MathSciNet review: 0316238
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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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DOI: https://doi.org/10.1090/S0002-9939-1973-0316238-1
Keywords: Generic structure, model companion, model completion, categorical theory, $ {\aleph _0}$-categorical abelian group
Article copyright: © Copyright 1973 American Mathematical Society