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A universality result for endomorphism monoids of some ultrahomogeneous structures

Published online by Cambridge University Press:  16 March 2012

Igor Dolinka
Affiliation:
Department of Mathematics and Informatics, University of Novi Sad, Trg Dositeja Obradovića 4, 21000 Novi Sad, Serbia ([email protected]; [email protected])
Dragan Mašulović
Affiliation:
Department of Mathematics and Informatics, University of Novi Sad, Trg Dositeja Obradovića 4, 21000 Novi Sad, Serbia ([email protected]; [email protected])
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Abstract

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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.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2012

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