Submission date: 24 November 2020

Abstract:

Fix an abelian group Γ and an injective endomorphism F : Γ → Γ. Improving on the results of Bell and Moosa, new characterizations are here obtained for the existence of spanning sets, F-automaticity, and F-sparsity. The model theoretic status of these sets is also investigated, culminating with a combinatorial description of the F-sparse sets that are stable in (Γ, +), and a proof that the expansion of (Γ, +) by any F-sparse set is NIP. These methods are also used to show for prime p ≥ 7 that the expansion of (𝔽_p[t], +) by multiplication restricted to t^ℕ is NIP.

Mathematics Subject Classification: 03C45 (Primary) 11B85, 68Q45 (Secondary)

Keywords and phrases:

Full text arXiv 2011.12405: pdf, ps.