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2 results

  • RETRACTIONS OF REVERSIBLE STRUCTURES

  • MILOŠ S. KURILIĆ
  • Journal:
    The Journal of Symbolic Logic / Volume 82 / Issue 4 / December 2017
    Published online by Cambridge University Press:
    09 January 2018, pp. 1422-1437
    Print publication:
    December 2017

  • A relational structure is called reversible iff each bijective endomorphism (condensation) of that structure is an automorphism. We show that reversibility is an invariant of some forms of L∞ω −bi-interpretability, implying that the condensation monoids of structures are topologically isomorphic. Applying these results, we prove that, in particular, all orbits of ultrahomogeneous tournaments and reversible ultrahomogeneous m-uniform hypergraphs are reversible relations and that the same holds for the orbits of reversible ultrahomogeneous digraphs definable by formulas which are not R-negative.

  • FRAÏSSÉ LIMITS OF METRIC STRUCTURES

  • ITAÏ BEN YAACOV
  • Journal:
    The Journal of Symbolic Logic / Volume 80 / Issue 1 / March 2015
    Published online by Cambridge University Press:
    13 March 2015, pp. 100-115
    Print publication:
    March 2015

  • We develop Fraïssé theory, namely the theory of Fraïssé classes and Fraïssé limits, in the context of metric structures. We show that a class of finitely generated structures is Fraïssé if and only if it is the age of a separable approximately homogeneous structure, and conversely, that this structure is necessarily the unique limit of the class, and is universal for it.

    We do this in a somewhat new approach, in which “finite maps up to errors” are coded by approximate isometries.