A Dependent Bi-Coloured Field

TL;DR

This paper studies a class of ordered real fields with a color predicate, constructs a Fraisse limit, and analyzes its model-theoretic properties, showing it is dependent but non-distal with infinite dp-rank.

Contribution

It introduces a new Fraisse class of colored ordered real fields and establishes their dependence and non-distality properties.

Findings

The theory is dependent.

The theory is non-distal.

The dp-rank is countably infinite.

Abstract

We have considered a Fraisse class of finitely generated ordered real fields with a colour predicate. A predimension map is defined on finite sets and the Fraisse limit of the class is axiomatized by a theory $T$, which is proved to be dependent. The theory is proved to be non-distal with $dp-rank=\aleph_0$.