## A discrete representation of free MV-algebras

We prove that the $n$-generated free MV-algebra is isomorphic to a quotient of the disjoint union of all the $n$-generated free MV$^{(n)}$-algebras. Such a quotient can be seen as the direct limit of a system consisting of all free MV${}^{(n)}$-algebras and special maps between them as morphisms.

A discrete representation of free MV-algebras