arXiv subjects

Melissa Özsahakyan

Publications and source records attributed to Melissa Özsahakyan.

2 recordsLinked to original sources

arXiv2026

VC-Density in Divisible Oriented Abelian Groups and Their Pairs

We show that the VC-density in certain theories of oriented abelian groups is at most the size of parameter variables, which yields dp-minimality. We further prove that the VC-density of formulas in pairs of such models is bounded by twice the size of parameter variables. This uniform upper bound is shown to be sharp, and as a consequence, we show that such pairs have dp-rank 2.

math.LO↗

arXiv2021

Expansions of the Group of Integers by Beatty Sequences

We study the model theoretic structure $(\Z,+,P_r)$ where $r>1$ is an irrational number and the elements of $P_r$ are of the form $\floor{nr}$ for some $n\in\Z\setminus\{0\}$. We axiomatize of this structure and prove a quantifier elimination result. As a consequence, we get that definable subsets are not sparse unless they are finite. We also prove that there are no reducts of this structure expanding $(\Z,+)$.

math.LO↗