Abstract

We analyze the logical strength of theorems on marriage problems with unique solutions using the techniques of reverse mathematics, restricting our attention to problems in which each boy knows only finitely many girls. In general, these marriage theorems assert that if a marriage problem has a unique solution then there is a way to enumerate the boys so that for every m, the first m boys know exactly m girls. The strength of each theorem depends on whether the underlying marriage problem is finite, infinite, or bounded.