The talk starts with a surveys of some recent connections between logic and discrete mathematics. Then we discuss logics which model the passage between an infinite sequence of finite models to an uncountable limiting object, such as is the case in the context of graphons. Of particular interest is the connection between the countable and the uncountable object that one obtains as the union versus the combinatorial limit of the same sequence. We compare such logics and discuss some consequences of such comparisons, as well as some hopes for further results in this research proje
