 ##  [Keisler Order](/keisler-order) 

  ##  [Keisler Order](https://mathlogic.quantumdictionary.io/keisler-order-0) 

  
 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural &amp; Formal Sciences -

**Mathematics &amp; Logic Dictionary**

 
Definition

A pre‑order on complete first‑order theories that compares their relative complexity by testing which theories have saturated ultrapowers with respect to classes of regular ultrafilters: T1 ≤ T2 if every regular ultrafilter that saturates T2 also saturates T1.