Extending partial isomorphisms on finite structures

Abstract

We prove the following theorem: Let A be a finite structure in a fixed finite relational language,p 1,...,p m partial isomorphisms of A. Then there exists a finite structure B, and automorphismsf i of B extending thep i 's. This theorem can be used to prove the small index property for the random structure in this language. A special case of this theorem is, if A and B are hypergraphs. In addition we prove the theorem for the case of triangle free graphs.