The exogenous semantic approach for enriching a given base logic was introduced by P. Mateus e A. Sernadas in order to obtain an exogenous quantum logic that extends classical propositional logic. Along this enrichment, we can distinguish two intermediate steps, globalization and probabilization. In this work we will focus on presenting globalization as a mechanism for enriching a given base logic, using the key idea of taking, as global models, sets of models of the base logic. We will then study preservation results, such as completeness and algebraizability. Joint work with Carlos Caleiro.