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.

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Herwig, B. Extending partial isomorphisms on finite structures. Combinatorica 15, 365–371 (1995). https://doi.org/10.1007/BF01299742

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Mathematics Subject Classification (1991)

  • 05 C 25
  • 05 C 65
  • 08 A 35