Saturated Model

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.

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.