A universality result for endomorphism monoids of some ultrahomogeneous structures

Abstract

We devise a fairly general sufficient condition ensuring that the endomorphism monoid of a countably infinite ultrahomogeneous structure (i.e. a Fra\"ıssé limit) embeds all countable semigroups. This approach provides us not only 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.

arXiv comment20 pages; to appear in the Proceedings of the Edinburgh Mathematical Society