Definable groups in models of Presburger Arithmetic

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 (Z,+,<) of Presburger Arithmetic i...

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Bibliographic Details
Published inAnnals of pure and applied logic Vol. 171; no. 6; p. 102795
Main Authors Onshuus, Alf, Vicaría, Mariana
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.06.2020
Subjects
Amenable groups
Definable groups
Presburger arithmetic
Definable groups
03C64
03C65
03C10
03C45
Presburger arithmetic
Amenable groups
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Summary: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 (Z,+,<) of Presburger Arithmetic is definably isomorphic to (Z,+)n mod out by a lattice.
ISSN:0168-0072
DOI:10.1016/j.apal.2020.102795