The Gödel-Tarski translation tr(A) of a propositional formula A is the result of prefixing \(\square\) to all subformulas of A. For any superintuitionistic logic L the least modal logic containing tr(A) for all A in L is denoted by \(\tau\) L. The author proves, using his model- theoretic techniques, that the finite model property, Kripke completeness, disjunctive properties and decidability hold for \(\tau\) L if they hold for L. Some of these result were previously proved by different methods.