# Prime model

From Encyclopedia of Mathematics

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.

**How to Cite This Entry:**

Prime model.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Prime_model&oldid=31517

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