 Model complete theory

A theory is model-complete when every embedding between its models is elementary. Every model-complete theory is inductive and hence admits a forall-exists axiomatization.

In mathematical logic, a **model complete theory** is a type of first-order theory that has a specific structure regarding its models. A theory \( T \) is called model complete if every embedding (i.e., a structure-preserving map) between any two models of \( T \) is an isomorphism when the models are elementarily equivalent.