Extending partial isomorphisms on finite structures


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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  1. [1]

    P. Cameron: Oligomorphic Permutation Groups, LMSLNS 152, Cambridge University Press, 1990.

  2. [2]

    E. Hrushovski: Extending Partial Isomorphisms of Graphs,Combinatorica 12 (1992), 411–416.

    Google Scholar 

  3. [3]

    Hodges, Hodkinson, Lascar, Shelah: The Small Index Property for ω-stable, ω-categorical, structures and for the random graph,Journal of the LMS,48 (1993), 204–218.

    Google Scholar 

  4. [4]

    J. K. Truss: Generic Automorphisms of Homogeneous Structures,Proceddings of the LMS (Ser. III),65 (1992), 121–141.

    Google Scholar 

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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