High Quality Content by WIKIPEDIA articles! In mathematical logic, and particularly in its subfield model theory, a saturated model M is one which realizes as many complete types as may be "reasonably expected" given its size.Let be a finite or infinite cardinal number and M a model in some first-order language. Then M is called -saturated if for all subsets A M of cardinality less than , M realizes all complete types over A. The model M is called saturated if it is |M|-saturated where |M| denotes the cardinality of M. That is, it realizes all complete types over sets of parameters of size less than |M|. According to some authors, a model M is called countably saturated if it is aleph_1-saturated; that is, it realizes all complete types over countable sets of parameters. According to others, it is countably saturated if it is aleph_0-saturated; i.e. realizes all complete types over finite parameter sets.

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