Year: 2026
Type: article
Abstract: Let k ≥ 2 $k\ge 2$ k greater than or equals 2 and let X be a subset of the natural numbers that is k -automatic and not eventually periodic. We show that the following dichotomy holds: either all k -automatic subsets are definable in the expansion of Presburger arithmetic in which we adjoin the predicate X , or ( N , + , X ) $(\mathbb {N},+,X)$ left parenthesis double struck upper N comma plus comma upper X right parenthesis has the same definable sets as ( N , + , k N ) $(\mathbb {N},+,k^{\mathbb {N}})$ left parenthesis double struck upper N comma plus comma k Superscript double struck upper N Baseline right parenthesis .
Source: Canadian Journal of Mathematics
Authors: Jason Bell, Alexi Block Gorman, Chris Schulz
Institutions: University of Waterloo, University of Amsterdam
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
OpenAlex ID: W7165772001
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