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ELIMINATION OF IMAGINARIES IN ORDERED ABELIAN GROUPS WITH BOUNDED REGULAR RANK

Part of: Model theory

Published online by Cambridge University Press:  06 February 2023

MARIANA VICARÍA Open the ORCID record for MARIANA VICARÍA [Opens in a new window]
MARIANA VICARÍA*
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF CALIFORNIA, LOS ANGELES LOS ANGELES, CA 90095, USA
*
E-mail: mariana_vicaria@berkeley.edu
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Abstract

In this paper we study elimination of imaginaries in some classes of 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 $\ell \Gamma $ in $\Gamma $, where $\ell \in \mathbb {N}_{\geq 2}$.

Keywords

elimination of imaginariesordered abelian groups

MSC classification

Primary: 03C64: Model theory of ordered structures; o-minimality 03C68: Other classical first-order model theory
Type
Article
Information
The Journal of Symbolic Logic , Volume 88 , Issue 4 , December 2023 , pp. 1639 - 1654
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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