A formula φ is strongly minimal if φ has Morley rank and Morley degree one. A structure M is strongly minimal if the formula x = x is.

Note that M is strongly minimal just in case it is infinite and for any elementary extension N of M and any N-definable subset X ⊆ N of N either X or N - X is finite.

Strongly minimal structures are at once the simplest examples of totally transcendental structures and the constituents of general sturctures of finite Morley rank.

Algebraic closure in fields generalizes to model theoretic algebraic closure. In a strongly minimal structure, taking closure to be algebraic closure, one has a combinatorial pregeometry. In particular, if X, Y ⊆ M are two maximal algebraically independent subsets, then X and Y have the same cardinality, which we define to be the dimension of M, and acl(X) = M = acl(Y). These observations comprise the main steps of the proof (due to Marsh) that every strongly minimal theory is categorical in all cardinals greater than its own cardinality.

This classification theorem for strongly minimal sets underlies the Baldwin-Lachlan refinement of Morley's theorem.