On Finitely Presented Expansions of Computably Enumerable Semigroups
نویسنده
چکیده
Every computable universal algebra has a finitely presented expansion, but there are examples of finitely generated, computably enumerable universal algebras with no finitely presented expansions. It is natural to ask whether such examples can be found in well-known classes of algebras such as groups and semigroups. In this paper, we build an example of a finitely generated, infinite, computably enumerable semigroup with no finitely presented expansions. We also discuss other interesting computability theoretic properties of this semigroup. This paper is based on the invited talk given by B. Khoussainov at the Mal’cev meeting 2011 dedicated to the 60th birthday of Professor Sergei Goncharov.
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