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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
##### Keywords:
computable Boolean algebra; decidable Boolean algebra
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