The actual consolidation of mathematical logic in Latin America comes from a variety of perspectives, not the least the construction of a solid community of researchers. Fifteen SLALM (Simposio Latino Americano de Lógica Matemática), from 1970 till 2012, have being central for a solid glueing of that community. We will present in our talk a brief history of those SLALMs, underscoring both (i) the impetus of some central figures (Chuaqui, Cignoli, Da Costa, Caicedo, Di Prisco, amongst others) and (ii) the construction of a well-connected web of researchers between leading countries (Brazil, Colombia, Chile, Argentina). The result confirms the role of an oscillating pendulum, in the advancements of science, between local, individual, initiatives and global, community, weavings.