Low is a Dividing Line in Keisler's Order

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 $T^{\prime }⊴T$ then $T^{\prime }$ is low. We also show there is a minimal nonlow theory $T_{cas}$.

15 pages

References in corpus (1)

• Keisler's order has infinitely many classes

Cited by in corpus (1)

• On regular ultrafilters, Boolean ultrapowers, and Keisler's order