Submission date: 29 December 2016

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 group definable in a model (Z,+,<) of Presburger Arithmetic is definably isomorphic to (Z, +)^{n} mod out by a lattice.

Mathematics Subject Classification:

Keywords and phrases:

Full text arXiv 1612.09042: pdf, ps.