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A universality result for endomorphism monoids of some ultrahomogeneous structures

Part of: General theory of categories and functors Algebraic structures Model theory Semigroups

Published online by Cambridge University Press:  16 March 2012

Igor Dolinka  and
Dragan Mašulović
Igor Dolinka
Affiliation:
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)
Dragan Mašulović
Affiliation:
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)
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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.

Keywords

endomorphism monoidFraïssé limitpushout

MSC classification

Secondary: 20M20: Semigroups of transformations, etc. 03C15: Denumerable structures 08A35: Automorphisms, endomorphisms 18A30: Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.) 20M50: Connections of semigroups with homological algebra and category theory
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 55 , Issue 3 , October 2012 , pp. 635 - 656
Copyright
Copyright © Edinburgh Mathematical Society 2012

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