Let be a first order language and let be an -structure. Let , a subset of the domain of be a definable infinite set. Then is minimal iff every definable we have either is finite or is finite. We say that is minimal iff the domain of is a strongly minimal set.
We say that is strongly minimal iff for every , we have that is minimal. Thus if is a complete theory then we say is strongly minimal if it has some model (equivalently all models) which is strongly minimal.
Note that is strongly minimal iff every definable subset of is quantifier free definable in a language with just equality. Compare this to the notion of o-minimal structures.
|Date of creation||2013-03-22 13:27:13|
|Last modified on||2013-03-22 13:27:13|
|Last modified by||Timmy (1414)|