A decidable expansion of (Γ,+,F) with the independence property

2023/09/01 by Françoise Point, Point, Françoise
Computer Science · Mathematics · #03C45 #11B85 #68Q45 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2309.00392

openalex publication_date 2023/09/01 · openalex created_date 2023/09/05 · openalex updated_date 2026/07/28

Abstract

Let (Γ,+,F) be a finitely generated \mathbb 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 \mathcal F-sets defined by R. Moosa and T. Scanlon in "Am. J. Math. 126 (2004), no. 3, p. 473-522", where every automatic subset is definable.

Related

• F-sets and finite automata
• Contributions to the theory of F-automatic sets
• Bounded morphisms
• Automata and tame expansions of (ℤ,+)
• A characterization of those automata that structurally generate finite groups