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The lattice of deductive systems on Hilbert algebras. (English) Zbl 1010.03054
Summary: The concept of deductive system on a Hilbert algebra was introduced by A. Diego. We show that the set Ded \(\mathcal A\) of all deductive systems on a Hilbert algebra \(\mathcal A\) forms an algebraic lattice which is distributive.

MSC:
03G25 Other algebras related to logic
08A30 Subalgebras, congruence relations
03B22 Abstract deductive systems
03B20 Subsystems of classical logic (including intuitionistic logic)
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