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

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dc.creatorHoucine, Abderezak Ould
dc.date2008-04-17
dc.date.accessioned2026-07-07T09:33:24Z
dc.date.available2026-07-07T09:33:24Z
dc.descriptionWe 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.
dc.identifierhttps://arxiv.org/abs/0804.2908
dc.identifierhttp://arxiv.org/abs/0804.2908
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159123
dc.subjectLogic
dc.subjectGroup Theory
dc.titleOn Finitely Generated Models of Theories with at Most Countably Many Nonisomorphic Finitely Generated Models
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