A model is atomic when the complete type over the empty set of every finite tuple is isolated. For a complete theory in a countable language, a model is prime exactly when it is countable and atomic.
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A **prime model** is a concept from model theory, which is a branch of mathematical logic. Specifically, a prime model is a model of a particular theory that has a certain property of being "elementarily embeddable" into any other model of that theory.