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arXiv · 1009.2106

The Bergman property for endomorphism monoids of some Fra\"ıssé limits

Igor Dolinka
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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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Igor Dolinka. 2011-09-20. The Bergman property for endomorphism monoids of some Fra\"ıssé limits. https://doi.org/10.1515/form.2011.153

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