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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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