Monster Model

A deliberately large structure chosen to be highly saturated and strongly homogeneous so that every small model or type over a small parameter set embeds into it; used as a convenient universal domain for carrying out model-theoretic constructions and arguments.

A monster model is a chosen sufficiently large, highly saturated and strongly homogeneous model of a complete first-order theory that serves as a universal domain in which one works to compare, embed, and realize types over small parameter sets. It is a convenient ambient model rather than a unique canonical object.