Reversibility of extreme relational structures

  • Miloš S. Kurilić
  • Nenad MoračaEmail author


A relational structure \({{\mathbb {X}}}\) is called reversible iff each bijective homomorphism from \({{\mathbb {X}}}\) onto \({{\mathbb {X}}}\) is an isomorphism, and linear orders are prototypical examples of such structures. One way to detect new reversible structures of a given relational language L is to notice that the maximal or minimal elements of isomorphism-invariant sets of interpretations of the language L on a fixed domain X determine reversible structures. We isolate certain syntactical conditions providing that a satisfiable \(L_{\infty \omega }\)-theory defines a class of interpretations having extreme elements on a fixed domain and detect several classes of reversible structures. For some of these classes, we characterize the corresponding reversible extreme interpretations. In particular, we characterize the reversible countable ultrahomogeneous graphs.


Relational structure Reversible structure Maximal (minimal) structure Forbidden structure Infinitary language Ultrahomogeneous graphs 

Mathematics Subject Classification

03C30 03C52 03C98 05C63 05C20 



This research was supported by the Ministry of Education and Science of the Republic of Serbia (Project 174006).


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics and InformaticsUniversity of Novi SadNovi SadSerbia

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