Low is a Dividing Line in Keisler's Order

2017/04/05 by Douglas Ulrich, Ulrich, Douglas
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Limits and Structures in Graph Theory #Logic (math.LO) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1704.01537

openalex publication_date 2017/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Keisler's order has infinitely many classes

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• Some simple theories from a Boolean algebra point of view