Existence Theorem

An existence theorem is a theorem which asserts the existence of a certain object. The cited article explains that it might be a statement which begins with the phrase there exist, or a universal statement whose last quantifier is existential, and that in the formal terms of symbolic logic it is a theorem with a prenex normal form involving the existential quantifier, even though in practice such theorems are usually stated in ordinary mathematical language. It also records a controversy that goes back to the early twentieth century about purely theoretical existence theorems, which show that an object exists without providing a way to construct it. Theorems whose statement takes this form are grouped under this concept.