On Finitely Presented Expansions of Computably Enumerable
Semigroups
Status: published in Algebra
and Logic 51 (2012) 435 - 444.
Availability: journal
version amd preprint
Abstract. 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.
drh@math.uchicago.edu