When does one k-automatic set define another?

Chris Schulz, Department of Pure Mathematics, University of Waterloo

The k-automatic sets are those subsets of N^d whose base-k representations form a regular language. Building on theorems of Büchi and Bès, we aim to characterize the partial preorder among k-automatic sets of definability over (N, +). We give a conjecture—that this preorder contains exactly three equivalence classes—and discuss our progress toward proving this conjecture. This talk is based on joint work with Alexi Block Gorman (OSU) and Jason Bell (Waterloo).

MC 5479