Maksimova, L. L. Implicit definability and positive logics. (Russian, English) Zbl 1034.03008 Algebra Logika 42, No. 1, 65-93 (2003); translation in Algebra Logic 42, No. 1, 37-53 (2003). The author proves that there exist exactly 7 positive logics with the Projective Beth Property and gives their description. In addition, she proves decidability of the Projective Beth Property and of the Craig Interpolation Property in positive calculi extending Int\(^+\). These results and methods are applied to the study of extensions of the minimal Johansson logic. Reviewer: A. S. Morozov (Novosibirsk) Cited in 19 Documents MSC: 03B20 Subsystems of classical logic (including intuitionistic logic) 03B25 Decidability of theories and sets of sentences 03B55 Intermediate logics Keywords:implicit definability; positive logic; intuitionistic logic; superintuitionistic logic; projective Beth property; decidability; Craig interpolation property; extensions of the minimal Johansson logic PDFBibTeX XMLCite \textit{L. L. Maksimova}, Algebra Logika 42, No. 1, 65--93 (2003; Zbl 1034.03008); translation in Algebra Logic 42, No. 1, 37--53 (2003) Full Text: EuDML