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\({\aleph{}}_ 0\)-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.

MSC:

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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