Logic at the borderline of the millenium (Q2751809)

The author discusses the contemporary position of logic, having in mind the basic facts about its development during the last century. As he remarks, logic is apparently losing the quality of a science concerned with the correctness of reasoning and becoming a science about constructions having an extremely abstract nature. In this sense logic is transformed just into metalogic with its new role with the main point that logic comes out of limits of what is properly logical. In this short survey the following subjects are treated: closure operator and deductive systems, logical comprehension of the continuum, an extension of classical logic as a consequence of its restrictions, lattices of theories and logics, categories and topoi, closure operator and category together, algebraization of logic.NEWLINENEWLINEFor the entire collection see [Zbl 0960.00036].