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absolutely independent algebra 91 assume axiom of choice axiomatization BCK-algebras binary Boolean algebra Brouwerian semilattices calculus characterized classical logic complete congruence relation consequence contains contradiction Corollary countable define definition denotes distributive lattices distributive p-algebra element equational equivalent exists filter finite function functor Hence Heyting algebras homomorphism Idziak implication induction hypothesis intermediate logics intermediate predicate logics interpolation property intuitionistic logic isomorphic K-complete Kleene algebra Kripke frame language Lemma mapping Math Mathematical Logic meet irreducible MH-frame modal formula modal logic Moreover natural numbers negation nonstandard notion obtained operation paper partially ordered poset Prace z Logiki predicate logics preformulas problem proof of Theorem propositional logic propositional variable provable prove pseudocomplemented relative Stone relevant Reports on Mathematical result rules satisfaction class satisfies semantics semilattices sequent subalgebra subdirect subdirectly irreducible subformula subset subsystem Suppose symbols valid valuation variety wffs wp-Kleene algebras