Słowa kluczowe: Nelson’s logic, subintuitionistic logic, axiomatization, RM3, R-Mingle, relevant logics, quasi-relevant logics, RoutleyMeyer semantics, relational semantics, substructural logics, Referential Logics, Selfextensional Logics, Referential Semantics, Referential π-institutions, Selfextensional π-institutions, finite models, sl–semantics, completeness theorem, potential infinity, finite arithmetics, Distributive nearlattice, prime ideal, homomorphic image, Dedekind-infinite set, Peano system, Tarski-infinite set, Zermelo-Fraenkel set theory, Zermelo set theory with choice, deontic logic, intuitionistic logic, Instantiation overflow, predicative polymorphism, natural deduction, double-Heyting algebra, dual pseudocomplement, Heyting algebra with dual pseudocomplement, dually pseudocomplemented Heyting algebra, discriminator variety, semisimple, EDPC.