A universality result for endomorphism monoids of some ultrahomogeneous structures

Details A universality result for endomorphism monoids of some ultrahomogeneous structures A universality result for endomorphism monoids of some ultrahomogeneous structures

2010-09-15

arxiv.org/abs/1009.2892v2

Mathematics

Group Theory

20 pages; to appear in the Proceedings of the Edinburgh Mathematical Society

Scientific paper

We devise a fairly general sufficient condition ensuring that the endomorphism monoid of a countably infinite ultrahomogeneous structure (i.e. a Fra\"{\i}ss\'{e} 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.

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