This article aims to analyze the problem of the identity and persistence of objects based on the hylomorphic doctrine, that is, the doctrine according to which objects are mereological compositions of the elements of form and matter. After introducing the contemporary discussion on the problem of identity and persistence and identity of objects, we propose a brief formalism of the logic of the relationship between part and whole or mereology to define the solution to the problem under study that defines a possible solution for it.