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Prime model
open-in-new
<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, and in particular <a href="/facts/Model_theory/vLWVV8sQ">model theory</a>, a prime model is a <a href="/facts/Model_(mathematical_logic)/GsMx1fEb">model</a> that is as simple as possible. Specifically, a model P {\displaystyle P} is prime if it admits an <a href="/facts/Elementary_embedding/3C94AfFq">elementary embedding</a> into any model M {\displaystyle M} to which it is <a href="/facts/Elementarily_equivalent/3C94AfFq">elementarily equivalent</a> (that is, into any model M {\displaystyle M} satisfying the same <a href="/facts/Complete_theory/TfBN8Fnb">complete theory</a> as P {\displaystyle P} ). </p>