= Strongly minimal theory
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A <complete theory> with infinite models is strongly minimal when, in every model, each definable subset in one variable, with parameters allowed, is finite or <cofinite>. The requirement applies to all models and all parameter choices. The infinite-universe condition excludes trivial finite theories.
For an infinite set in the language of equality, a one-variable formula with finitely many parameters can only distinguish those named elements from the remaining elements, so every definable subset is finite or <cofinite>. In an <algebraically closed field>, <quantifier elimination> likewise makes every one-variable definable subset finite or <cofinite>, since a nonzero polynomial has finitely many roots. A <dense linear order without endpoints> fails this property: a proper open interval and its complement are both infinite. Strong minimality is a particularly restrictive source of <omega-stability>.
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