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Strongly constructive Boolean algebras. (Russian, English) Zbl 1096.03043
Algebra Logika 44, No. 1, 3-23 (2005); translation in Algebra Logic 44, No. 1, 1-12 (2005).
A computable model \(M\) is called \(n\)-constructive if there exists an algorithm that recognizes the \(\Sigma_n\)-formulas on elements of \(M\) true in \(M\). The model is called decidable if there exists an algorithm answering this question for all formulas.
For each complete extension \(T\) of the theory of Boolean algebras, the author finds the least \(n\) such that each \(n\)-constructive model of \(T\) has a decidable isomorphic copy.

MSC:
03C57 Computable structure theory, computable model theory
06E05 Structure theory of Boolean algebras
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