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

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

2008-04-17

arxiv.org/abs/0804.2908v1

Mathematics

Logic

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

On Finitely Generated Models of Theories with at Most Countably Many Nonisomorphic Finitely Generated Models does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On Finitely Generated Models of Theories with at Most Countably Many Nonisomorphic Finitely Generated Models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Finitely Generated Models of Theories with at Most Countably Many Nonisomorphic Finitely Generated Models will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-303515