All countable monoids embed into the monoid of the infinite random graph (Q960939)

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scientific article; zbMATH DE number 5687567
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All countable monoids embed into the monoid of the infinite random graph
scientific article; zbMATH DE number 5687567

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    All countable monoids embed into the monoid of the infinite random graph (English)
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    29 March 2010
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    From the authors summary: ``We prove that the full transformation monoid on a countably infinite set is isomorphic to a submonoid of \(\text{End}(R)\), the endomorphism monoid of the infinite random graph \(R\). Consequently, \(\text{End}(R)\) embeds each countable monoid, satisfies no nontrivial monoid identity, and has an undecidable universal theory.'' Note that the infinite random graph satisfies the existentially closed adjacency property, and it is a universal graph, i.e., each countable subgraph is isomorphic to an induced subgraph of \(R\).
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    infinite random graph
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    graph endomorphism
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    embedding
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