Melissa Özsahakyan (Imperial College London) – VC-Density in Oriented Abelian Groups and their Pair

Abstract: In this talk, we introduce oriented abelian groups and present some tameness properties of these structures and their pairs. We show that, in certain theories of oriented abelian groups, the VC-density of formulas is bounded by the size of parameter variable. We further show that, for a specific pair structure, this bound becomes twice the size of parameter variable, and that these bounds are optimal. This is joint work with Ebru Nayir.