‘Subalgebras of FA-presentable algebras’
[with N. Ruškuc]
Algebra Universalis, 72, no. 2 (October 2014), pp. 101–123.
DOI: 10.1007/s00012-014-0293-0. MR: 3257650. ZBL: 1321.08001.


Automatic presentations, also called FA-presentations, were introduced to extend finite model theory to infinite structures whilst retaining the solubility of fundamental decision problems. This paper studies FA-presentable algebras. First, an example is given to show that the class of finitely generated FA-presentable algebras is not closed under forming finitely generated subalgebras, even within the class of algebras with only unary operations. In contrast, a finitely generated subalgebra of an FA-presentable algebra with a single unary operation is itself FA-presentable. Furthermore, it is proven that the class of unary FA-presentable algebras is closed under forming finitely generated subalgebras, and that the membership problem for such subalgebras is decidable.