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RETRACTIONS OF REVERSIBLE STRUCTURES

Published online by Cambridge University Press:  09 January 2018

MILOŠ S. KURILIĆ*
Affiliation:
DEPARTMENT OF MATHEMATICS AND INFORMATICS UNIVERSITY OF NOVI SAD TRG DOSITEJA OBRADOVIĆA 4 21000 NOVI SAD, SERBIA E-mail: milos@dmi.uns.ac.rs

Abstract

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.

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Copyright
Copyright © The Association for Symbolic Logic 2017 

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