The existence of countable totally nonconstructive extensions of the countable atomless Boolean algebra

Journal of Symbolic Logic 48 (1):167-170 (1983)
Abstract
Our results concern the existence of a countable extension U of the countable atomless Boolean algebra B such that U is a "nonconstructive" extension of B. It is known that for any fixed admissible indexing φ of B there is a countable nonconstructive extension U of B (relative to φ). The main theorem here shows that there exists an extension U of B such that for any admissible indexing φ of B, U is nonconstructive (relative to φ). Thus, in this sense U is a countable totally nonconstructive extension of B
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