The Bergman property for endomorphism monoids of some Fraïssé limits

Details The Bergman property for endomorphism monoids of some Fraïssé limits The Bergman property for endomorphism monoids of some Fraïssé limits

2010-09-10

arxiv.org/abs/1009.2106v3

Mathematics

Group Theory

16 pages; to appear in Forum Mathematicum

Scientific paper

Based on an idea of Y. P\'eresse and some results of Maltcev, Mitchell and Ru\v{s}kuc, 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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