Prime Model

- Natural & Formal Sciences -
Mathematics & Logic Dictionary
A minimal model of a complete first-order theory that elementarily embeds into every other model of the theory; equivalently, a model generated by realizations of principal (isolated) types over the empty set.

Prime Model

- Pure Mathematics -
Algebra Dictionary
A model P of a complete theory T is prime if P elementarily embeds into every model of T; it is a minimal (with respect to elementary embeddings) canonical representative of the theory.