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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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