Uniqueness Theorem

A uniqueness theorem, also called a unicity theorem, is a theorem asserting the uniqueness of an object satisfying certain conditions, or the equivalence of all objects satisfying the said conditions. The cited article lists examples, among them Cauchy rigidity theorem and Alexandrov uniqueness theorem for three-dimensional polyhedra, the black hole uniqueness theorem, the Cauchy-Kowalevski theorem as the main local existence and uniqueness theorem for analytic partial differential equations, the division theorem on the uniqueness of quotient and remainder, and the fundamental theorem of arithmetic on the uniqueness of prime factorization. Theorems whose statement takes this form are grouped under this concept.