Difference between revisions of "Prime model"
From Encyclopedia of Mathematics
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| − | A model of an [[Elementary theory|elementary theory]] | + | {{TEX|done}} |
| + | A model of an [[Elementary theory|elementary theory]] $T$ that can be embedded in every model of $T$. If $T$ is model complete (cf. [[Model theory|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|prime field]] of that characteristic. | The prime model of the elementary theory of all fields with fixed characteristic is the [[Prime field|prime field]] of that characteristic. | ||
Latest revision as of 16:43, 11 April 2014
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
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