A characterization of retracts in certain Fraïssé limits. (English) Zbl 1247.03046
Summary: Assuming certain conditions on a class \(\mathcal C\) of finitely generated first-order structures admitting the model-theoretical construction of a Fraïssé limit, we characterize retracts of such limits as algebraically closed structures in a class naturally related to \(\mathcal C\). In this way we generalize an earlier description of retracts of the countably infinite random graph.
MSC:
| 03C15 | Model theory of denumerable and separable structures |
| 03C50 | Models with special properties (saturated, rigid, etc.) |
| 08A35 | Automorphisms and endomorphisms of algebraic structures |
Keywords:
Fraïssé limit; endomorphism; retract; algebraically closed structure; finitely generated structuresReferences:
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