Abstract:The properties of deductive systems in Hilbert algebras are treated. If a Hilbert algebra $H$ considered as an ordered set is an upper semilattice then prime deductive systems coincide with meet-irreducible elements of the lattice $Ded H$ of all deductive systems on $H$ and every maximal deductive system is prime. Complements and relative complements of $Ded H$ are characterized as the so called annihilators in $H$.
Keywords: (commutative) Hilbert algebra, deductive system (generated by a set), annihilator
AMS Subject Classification: 06A11, 03G25, 03B22