Definable sets up to definable bijections in Presburger groups

Abstract

We entirely classify definable sets up to definable bijections in $\mathbb{Z}$-groups, where the language is the one of ordered abelian groups. From this, we deduce, among others, a classification of definable families of bounded definable sets.

References in corpus (1)

• Classification of semi-algebraic $p$-adic sets up to semi-algebraic bijection