Submission date: 1 September 2023

Abstract:

Let (Γ,+,F) be a finitely generated ℤ[F]-module where F is an injective endomorphism of the abelian group Γ. We restrict ourselves to a finite automa presentable subclass, introduced by J. Bell and R. Moosa in “F-sets and finite automata. J. Théor. Nombres Bordeaux 31 (2019), no. 1, 101-130” and define an expansion containing the F-sets defined by R. Moosa and T. Scanlon in &$#147;Am. J. Math. 126 (2004), no. 3, p. 473-522”, where every automatic subset is definable.

Mathematics Subject Classification: 03C45, 11B85, 68Q45

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