Abstract
Publisher Summary This chapter describes the homogeneous directed graphs, which fall naturally into three families: deficient, imprimitive, and freely generated. The imprimitive ones are classified in the chapter. A relational system ‘H’ is said to be homogeneous if any isomorphism between two of its finite substructures is induced by an automorphism of H. The stable homogeneous structures for a fixed finite relational language fall into finitely many families, with the isomorphism type of the structures within a family determined by rather trivial numerical invariants. In particular, there are only many countable stable homogeneous structures for a given finite relational language.
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