Proceedings of the Edinburgh Mathematical Society (Series 2)

Table of Contents - October 2012 - Volume 55, Issue 03  

Research Article

A universality result for endomorphism monoids of some ultrahomogeneous structures

Igor Dolinkaa1 and Dragan Mašulovića1

a1 Department of Mathematics and Informatics, University of Novi Sad, Trg Dositeja Obradovića 4, 21000 Novi Sad, Serbia (dockie@dmi.uns.ac.rs; masul@dmi.uns.ac.rs)

Abstract

We devise a fairly general sufficient condition ensuring that the endomorphism monoid of a countably infinite ultrahomogeneous structure (i.e. a Fraïssé limit) embeds all countable semigroups. This approach not only provides us with a framework unifying the previous scattered results in this vein, but actually yields new applications for endomorphism monoids of the (rational) Urysohn space and the countable universal ultrahomogeneous semilattice.

(Received September 15 2010)

Keywords

  • endomorphism monoid;
  • Fraïssé limit;
  • pushout

2010 Mathematics subject classification

  • Primary 20M20;
  • Secondary 03C15;
  • 08A35;
  • 18A30;
  • 20M50