A Dichotomy for $k$-automatic expansions of Presburger Arithmetic

📝 Original Info

• Title: A Dichotomy for $k$-automatic expansions of Presburger Arithmetic
• ArXiv ID: 2508.04851
• Date: 2025-08-06
• Authors: ** 논문에 명시된 저자 정보가 제공되지 않았습니다. (가능하면 원문에서 확인 필요) **

📝 Abstract

Let $k\ge 2$ and let $X$ be a subset of the natural numbers that is $k$-automatic and not eventually periodic. We show that a dichotomy holds: either all $k$-automatic subsets are definable in the expansion of Presburger arithmetic in which we adjoin the predicate $X$, or $(\mathbb{N},+,X)=(\mathbb{N},+,k^{\mathbb{N}})$.

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