Rigid models of Presburger arithmetic

TL;DR

This paper characterizes rigid models of Presburger arithmetic, showing they exist for all infinite sizes up to the continuum but not beyond, providing insights into the structure of these models.

Contribution

It offers a complete description of the sizes of rigid models of Presburger arithmetic, highlighting their existence and limitations.

Findings

Rigid models exist for all infinite cardinalities up to the continuum.

No rigid models exist for larger cardinalities.

The paper provides a structural characterization of these models.

Abstract

We present a description of rigid models of Presburger arithmetic (i.e., Z-groups). In particular, we show that Presburger arithmetic has rigid models of all infinite cardinalities up to the continuum, but no larger.