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On a sufficient condition for strong constructivizability of atomic Boolean algebras. (Russian) Zbl 1029.03023
The main result reads as follows: Assume $$(\mathfrak{B},\nu)$$ is a constructive Boolean algebra and $$J$$ is its ideal whose set of all $$\nu$$-numbers is $$\Delta_2^0$$. Then there exists a strongly constructive Boolean algebra $$\mathfrak{A}$$ such that $$\mathfrak{B}/J\cong\mathfrak{A}/\Phi$$, where $$\Phi$$ is the Frechét ideal of $$\mathfrak{A}$$.
In particular, the author proves as a corollary that any constructive Boolean algebra whose Frechét ideal is in $$\Delta_2^0$$ possesses a strong constructivization.
##### MSC:
 03C57 Computable structure theory, computable model theory 03D45 Theory of numerations, effectively presented structures 06E05 Structure theory of Boolean algebras
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