A model companion of a first-order theory 
is a model-complete theory 
such that every model of 
embeds in a model of 
and every model of 
embeds in a model of 
. When it exists, a model companion is unique up to logical
equivalence.
Model Companion
See also
Model Completeness, Model Completion, Model TheoryExplore with Wolfram|Alpha
References
Hodges, W. A Shorter Model Theory. New York: Cambridge University Press, 1997.Cite this as:
Weisstein, Eric W. "Model Companion." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ModelCompanion.html