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We show an effective cut-free variant of Glivenko's theorem extended to formulas with weak quantifiers: "There is an elementary function f such that if φ is a cut-free LK proof of ⊢ A with symbol complexity ≤ c, then there exists a cut-free LJ proof of ⊢ &#x22AF &#x22AF A with symbol complexity ≤ f(c)"...
We show that the model checking problem for intuitionistic propositional logic with one variable is complete for logspace-uniform AC 1. For superintuitionistic logics with one variable, we obtain NC 1-completeness for the model checking problem.
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