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We study finitely generated models of countable theories, having at mostcountably many nonisomorphic finitely generated models. We intro- duce a notionof rank of finitely generated models and we prove, when T has at most countablymany nonisomorphic finitely generated models, that every finitely generatedmodel has an ordinal rank. This rank is used to give a prop- erty of finitelygenerated models analogue to the Hopf property of groups and also to give anecessary and sufficient condition for a finitely generated model to be primeof its complete theory. We investigate some properties of limit groups ofequationally noetherian groups, in respect to their ranks.

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