Prime model

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A model of an elementary theory $T$ that can be embedded in every model of $T$. If $T$ is model complete (cf. Model theory) and admits a prime model, then $T$ is complete. This fact is called the prime model test.

The prime model of the elementary theory of all fields with fixed characteristic is the prime field of that characteristic.

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Prime model. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by F.-V. Kuhlmann (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article