A first-order theory is model complete if every embedding between any two of its models is an elementary embedding. Equivalently, every formula is equivalent modulo the theory to an existential formula.
Model Completeness
See also
Model Companion, 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 Completeness." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ModelCompleteness.html