On a sufficient condition for strong constructivizability of atomic Boolean algebras. (Russian) Zbl 1029.03023

Dzgoev, V. D.

Vladikavkaz. Mat. Zh. 2, No. 2, 10-18 (2000).

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.

Reviewer: A.S.Morozov (Novosibirsk)

MSC:

03C57	Computable structure theory, computable model theory
03D45	Theory of numerations, effectively presented structures
06E05	Structure theory of Boolean algebras

Keywords:

constructive Boolean algebra; recursive model; Frechét ideal