General Events - Department of Mathematics

The k-automatic sets, those whose base-k representations form a regular language, are a well-studied class of subsets of the natural numbers. In this talk, we discuss our proof of the following dichotomy: given a k-automatic subset X of the natural numbers, either X is definable from Presburger arithmetic expanded by a predicate for the powers of k, or else the Presburger arithmetic expanded by X itself defines any other k-automatic set. This talk is based on joint work with Jason Bell and Alexi Block Gorman.