The study of propositional realizability logic was initiated in the 50th of the last century. Some interesting results were obtained in the 60-70th, but many important problems in this area are still open. Now interest to these problems from new generation of researchers is observed. This survey contains an exposition of the results on propositional realizability logic and corresponding techniques. Thus reading this paper can be the start point in exploring and development of constructive logic.

We discuss the work of Paul Bernays in set theory, mainly his axiomatization and his use of classes but also his higher-order reflection principles.

We classify actions of groups of finite Morley rank on abelian groups of Morley rank 2: there are essentially two, namely the natural actions of SL(V) and GL(V) with V a vector space of dimension 2. We also prove an identification theorem for the natural module of SL₂ in the finite Morley rank category.