Strongly minimal theory

Summary

A strongly minimal theory is a complete first-order theory with infinite models. In each of its models, every definable subset of the line is finite or cofinite. These theories are the simplest infinite structures from the point of view of definability. In a strongly minimal theory, algebraic closure behaves like linear span, so each model has a well-defined dimension. They are basic building blocks of stable theories and are central to the study of categorical theories.