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Enumeration in algebra

We show how the concept of enumeration reducibility from comput-ability theory may be applied to obtain computability conditions on descriptions of substructures of algebras, more prominently on the language of forbidden words of a subshift, and on the word problem for finitely generated groups. Many of the results here are already known for recursively presented groups and effectively closed subshifts, but using enumeration reducibility we are able to generalize them to arbitrary objects. The proof is based on a topological framework similar to universal algebra, and generalizes in particular work by Kuznetsov and others.