Definable groups in models of Presburger Arithmetic

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Annals of Pure and Applied Logic 171 (6):102795 (2020)
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Abstract

This paper is devoted to understand groups definable in Presburger Arithmetic. We prove the following theorems: Theorem 1. Every group definable in a model of Presburger Arithmetic is abelian-by-finite. Theorem 2. Every bounded abelian group definable in a model of (Z, +, <) Presburger Arithmetic is definably isomorphic to (Z, +)^n mod out by a lattice.

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10.1016/j.apal.2020.102795

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Citations of this work

Groups definable in Presburger arithmetic.Juan Pablo Acosta - 2025 - Annals of Pure and Applied Logic 176 (1):103507.

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References found in this work

Characterizing Rosy Theories.Clifton Ealy & Alf Onshuus - 2007 - Journal of Symbolic Logic 72 (3):919 - 940.
Quasi-o-minimal structures.Oleg Belegradek, Ya'acov Peterzil & Frank Wagner - 2000 - Journal of Symbolic Logic 65 (3):1115-1132.
Presburger sets and p-minimal fields.Raf Cluckers - 2003 - Journal of Symbolic Logic 68 (1):153-162.
Forking and independence in o-minimal theories.Alfred Dolich - 2004 - Journal of Symbolic Logic 69 (1):215-240.

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