Low is a Dividing Line in Keisler's Order

TL;DR

This paper proves that low theories form a dividing line in Keisler's order within ZFC, establishing a hierarchy and identifying a minimal nonlow theory.

Contribution

It demonstrates that the class of low theories is a dividing line in Keisler's order and identifies a minimal nonlow theory, advancing understanding of model-theoretic classification.

Findings

Low theories form a dividing line in Keisler's order.

Existence of a minimal nonlow theory $T_{cas}$.

The dividing line property holds in ZFC.

Abstract

We show in $ZFC$ that the class of low theories forms a dividing line in Keisler's order. That is, if $T$ is low and $T' \trianglelefteq T$ then $T'$ is low. We also show there is a minimal nonlow theory $T_{cas}$.