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On Finitely Generated Models of Theories with at Most Countably Many Nonisomorphic Finitely Generated Models

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 نشر من قبل Abderezak Ould Houcine
 تاريخ النشر 2008
  مجال البحث
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We study finitely generated models of countable theories, having at most countably many nonisomorphic finitely generated models. We intro- duce a notion of rank of finitely generated models and we prove, when T has at most countably many nonisomorphic finitely generated models, that every finitely generated model has an ordinal rank. This rank is used to give a prop- erty of finitely generated models analogue to the Hopf property of groups and also to give a necessary and sufficient condition for a finitely generated model to be prime of its complete theory. We investigate some properties of limit groups of equationally noetherian groups, in respect to their ranks.



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