A. Gorman

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math.LO2026

O-minimal open core is not an elementary property

Alexi Block Gorman, Esther Elbaz Saban

Given a structure $M$ 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…

math.LO2026

A Dichotomy for $k$ -automatic expansions of Presburger Arithmetic

Jason Bell, Alexi Block Gorman, Chris Schulz

Let $k \geq 2$ 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…

math.LO2025

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 $[0, 1]$ whose base- $r$ representations are recognized by a BÃ¼chi automaton. In…

O-minimal open core is not an elementary property

A Dichotomy for k-automatic expansions of Presburger Arithmetic

Sparse regular subsets of the reals

A Dichotomy for $k$ -automatic expansions of Presburger Arithmetic