Expansion of Presburger arithmetic with the exchange property

2018/06/01 by Nathanaël Mariaule, Mariaule, Nathanaël
Computer Science · Mathematics · #03C64 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis #math.LO #msc:03C64

paper · pdf · doi:10.48550/arxiv.1806.00315

10 pages

arxiv created 2018/06/01 · openalex publication_date 2018/06/01 · arxiv updated 2018/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a model of Presburger arithmetic. Let L be an expansion of the language of Presburger L_Pres. In this paper we prove that the L-theory of G is L_Pres-minimal iff it has the exchange property and any bounded definable set has a maximum.

Related

• A survival guide to presburger arithmetic
• Presburger sets and p-minimal fields
• Definable groups in models of Presburger Arithmetic and G⁰⁰
• Subclasses of presburger arithmetic and the weak EXP hierarchy
• Undefinability of multiplication in Presburger arithmetic with sets of powers