Hostname: page-component-745bb68f8f-kw2vx Total loading time: 0 Render date: 2025-02-08T21:17:38.187Z Has data issue: false hasContentIssue false
  • English
  • Français

RETRACTIONS OF REVERSIBLE STRUCTURES

Published online by Cambridge University Press:  09 January 2018

MILOŠ S. KURILIĆ
MILOŠ S. KURILIĆ*
Affiliation:
DEPARTMENT OF MATHEMATICS AND INFORMATICS UNIVERSITY OF NOVI SAD TRG DOSITEJA OBRADOVIĆA 4 21000 NOVI SAD, SERBIAE-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

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.

Keywords

03C0703C4003C5003C9805C6305C20bijective endomorphismreversible structurebi-interpretabilityultrahomogeneous structureorbitautomorphism group
Type
Articles
Information
The Journal of Symbolic Logic , Volume 82 , Issue 4 , December 2017 , pp. 1422 - 1437
Copyright
Copyright © The Association for Symbolic Logic 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Ahlbrandt, G. and Ziegler, M., Quasi-finitely axiomatizable totally categorical theories, stability in model theory (Trento, 1984). Annals of Pure and Applied Logic, vol. 30 (1986), no. 1, pp. 63–82.Google Scholar
Cameron, P. J., Transitivity of permutation groups on unordered sets. Mathematische Zeitschrift, vol. 148 (1976), no. 2, pp. 127–139.CrossRefGoogle Scholar
Cameron, P. J., The random graph, The Mathematics of Paul Erdös II (Graham, R. L. and Nešetřil, J., editors), Algorithms and Combinatorics, vol. 14, Springer, Berlin, 1997, pp. 333–351.Google Scholar
Doyle, P. C., and Hocking, J. G., Bijectively related spaces. I. Manifolds. Pacific Journal of Mathematics, vol. 111 (1984), no. 1, pp. 23–33.Google Scholar
Fraïssé, R., Theory of Relations, revised ed., Studies in Logic and the Foundations of Mathematics, vol. 145, North-Holland, Amsterdam, 2000.Google Scholar
Henson, C. W., A family of countable homogeneous graphs. Pacific Journal of Mathematics, vol. 38 (1971), pp. 69–83.Google Scholar
Henson, C. W., Countable homogeneous relational structures and ${\aleph _0}$ -categorical theories, this Journal, vol. 37 (1972), pp. 494–500.Google Scholar
Hodges, W., Model Theory, Encyclopedia of Mathematics and its Applications, vol. 42, Cambridge University Press, Cambridge, 1993.Google Scholar
Kukiela, M., Reversible and bijectively related posets. Order, vol. 26 (2009), no. 2, pp. 119–124.Google Scholar
Kurilić, M. S., Reversibility of definable relations, to appear.Google Scholar
Kurilić, M. S., and Morača, N., Condensational equivalence, equimorphism, elementary equivalence and similar similarities. Annals of Pure and Applied Logic, vol. 168 (2017), no. 6, pp. 1210–1223.Google Scholar
Kurilić, M. S., and Morača, N., Reversibility of extreme structures, to appear.Google Scholar
Kurilić, M. S., and Morača, N., Variations of reversibility, to appear.Google Scholar
Kurilić, M. S., and Morača, N., Reversibility of disconnected structures, to appear.Google Scholar
Lachlan, A. H., Countable homogeneous tournaments. Transactions of the American Mathematical Society, vol. 284 (1984), no. 2, pp. 431–461.Google Scholar
Lachlan, A. H., and Woodrow, R. E., Countable ultrahomogeneous undirected graphs. Transactions of the American Mathematical Society, vol. 262 (1980), no. 1, pp. 51–94.Google Scholar
Lyndon, R. C., Properties preserved under homomorphism. Pacific Journal of Mathematics, vol. 9 (1959), pp. 143–154.Google Scholar
Macpherson, D., A survey of homogeneous structures. Discrete Mathematics, vol. 311 (2011), no. 15, pp. 1599–1634.Google Scholar
Rajagopalan, M., and Wilansky, A., Reversible topological spaces. Journal of the Australian Mathematical Society, vol. 6 (1966), pp. 129–138.Google Scholar