Sparse subsets of the reals

Jason Bell, Department of Pure Mathematics, University of Waterloo

We look at the first-order theory of the real numbers augmented by a predicate X that is in some natural sense self-similar with respect to a positive integer base. We show that there is a dichotomy: either we can define a Cantor set in our structure or our expansion of the reals is interdefinable with the real numbers augmented by a set of the form {1/r, 1/r^2, 1/r^3, …} for some integer r>=2.  In the latter case, this is equivalent to the structure having NIP and NTP_2.  This is joint work with Alexi Block Gorman.

MC 5479