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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.

MSC:

03B20 Subsystems of classical logic (including intuitionistic logic)
03B25 Decidability of theories and sets of sentences
03B55 Intermediate logics
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