\({\aleph{}}_ 0\)-categorical tree-decomposable structures. (English) Zbl 0765.03017

The main scope of this note is to study countable \(\aleph_ 0\)- categorical structures whose theories are tree-decomposable in the sense of Baldwin and Shelah. The permutation group corresponding to such a structure can be decomposed in a canonical manner into simpler permutation groups in the same class. As an application of the analysis, it is proved that these structures are finitely homogeneous.


03C35 Categoricity and completeness of theories
20B07 General theory for infinite permutation groups
03C15 Model theory of denumerable and separable structures
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