##  [Saturated Model](/saturated-model) 

  ##  [Saturated Model](https://mathlogic.quantumdictionary.io/saturated-model-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 & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A model that realizes every type over parameter sets of cardinality below its saturation cardinal; informally, a model is κ-saturated if it realizes all types over parameter sets of size less than κ, and saturated when κ equals its own cardinality.

 

 

 

 

 





 

 



 ##  [Saturated Model](https://algebra.quantumdictionary.io/saturated-model-1) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A model M is κ‑saturated (for a cardinal κ) if every consistent type over any parameter set of size less than κ is realized in M; informally, M is as rich as possible relative to its size in that it realizes all small types.