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2009 Isomorphism of Homogeneous Structures
John D. Clemens
Notre Dame J. Formal Logic 50(1): 1-22 (2009). DOI: 10.1215/00294527-2008-024


We consider the complexity of the isomorphism relation on countable first-order structures with transitive automorphism groups. We use the theory of Borel reducibility of equivalence relations to show that the isomorphism problem for vertex-transitive graphs is as complicated as the isomorphism problem for arbitrary graphs and determine for which first-order languages the isomorphism problem for transitive countable structures is as complicated as it is for arbitrary countable structures. We then use these results to characterize the complexity of the isometry relation for certain classes of homogeneous and ultrahomogeneous metric spaces.


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John D. Clemens. "Isomorphism of Homogeneous Structures." Notre Dame J. Formal Logic 50 (1) 1 - 22, 2009.


Published: 2009
First available in Project Euclid: 19 January 2009

zbMATH: 1188.03031
MathSciNet: MR2536697
Digital Object Identifier: 10.1215/00294527-2008-024

Primary: 03E15
Secondary: 03C15 , 03C50

Keywords: countable structures , homogeneous , isomorphism

Rights: Copyright © 2009 University of Notre Dame

Vol.50 • No. 1 • 2009
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