Mariana Vicaría (UCLA)

Elimination of imaginaries in ordered abelian groups of bounded regular rank

Note time change: 4pm

In this talk I will present some results about elimination of imaginaries in pure ordered abelian groups. For the class of ordered abelian groups with bounded regular rank (equivalently with finite spines) we obtain weak elimination of imaginaries once we add sorts for the quotient groups $\Gamma/ \Delta$ for each definable convex subgroup $\Delta$, and sorts for the quotient groups $\Gamma/(\Delta+ \ell\Gamma)$ where $\Delta$ is a definable convex subgroup and $\ell \in \mathbb{N}_{\geq 2}$. We refer to these sorts as the quotient sorts. For the dp-minimal case we obtain a complete elimination of imaginaries if we also add constants to distinguish the cosets of $\Delta+\ell\Gamma$ in $\Gamma$, where $\Delta$ is a definable convex subgroup and $\ell \in \mathbb{N}_{\geq 2}$.

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