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The Bergman property for endomorphism monoids of some Fraïssé limits

Authors
  • Dolinka, Igor
Type
Published Article
Journal
Forum Mathematicum
Publisher
De Gruyter
Publication Date
Nov 10, 2011
Volume
26
Issue
2
Pages
357–376
Identifiers
DOI: 10.1515/form.2011.153
Source
De Gruyter
Keywords
License
Yellow

Abstract

Based on an idea of Y. Péresse and some results of Maltcev, Mitchell and Ruškuc, we present sufficient conditions under which the endomorphism monoid of a countably infinite ultrahomogeneous first-order structure has the Bergman property. This property has played a prominent role both in the theory of infinite permutation groups and, more recently, in semigroup theory. As a byproduct of our considerations, we establish a criterion for a countably infinite ultrahomogeneous structure to be homomorphism-homogeneous.

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