5 papers
O-minimal open core is not an elementary property
Alexi Block Gorman, Esther Elbaz Saban
Given a structure with a definable topology, its open core is a structure defined on the same universe whose language consists of all open sets of all arities definab…
A Dichotomy for -automatic expansions of Presburger Arithmetic
Jason Bell, Alexi Block Gorman, Chris Schulz
Let and let be a subset of the natural numbers that is -automatic and not eventually periodic. We show that the following dichotomy holds: either all -automatic…
Sequential densities of rational languages
Alexi Block Gorman, Dominique Perrin
We introduce the notion of density of a rational language with respect to a sequence of probability measures. We prove that if is a sequence of Bernoulli measures convergi…
One-sided Hom shifts
Marie-Pierre Béal, Alexi Block Gorman
We prove that it is decidable whether a one-sided shift of finite type is conjugate to a one-sided Hom-shift, and whether a tree-shift of finite type is conjugate to a Hom tree-shi…
Sparse regular subsets of the reals
Jason Bell, Alexi Block Gorman
This paper concerns the expansion of the real ordered additive group by a predicate for a subset of whose base- representations are recognized by a Büchi automaton. In…