The Saturated model reference article from the English Wikipedia on 24-Jul-2004 (provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

Saturated model

In mathematical logic, and in particular model theory, a model is -saturated if and only if it realizes all elements

, for

with .

A model is saturated if and only if it is -saturated, that is, it realizes all complete types over sets of parameters of size less than .

Saturated models exist: for instance, is saturated, the countable random graph is saturated. The natural numbers are not saturated: the type containing

is not realized in .

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