Strongly constructive Boolean algebras

A computable structure is said to be $n$-constructive if there exists an algorithm which, given a finite $\Sigma_n$-formula and a tuple of elements, determines whether that tuple satisfies this formula. A structure is strongly constructive if such an algorithm exists for all formulas of the predicate calculus, and is decidable if it has a strongly constructive isomorphic copy. We give a complete description of relations between $n$-constructibility and decidability for Boolean algebras of a fixed elementary characteristic.