Published online by Cambridge University Press: 12 March 2014
Our results concern the existence of a countable extension of the countable atomless Boolean algebra such that is a “nonconstructive” extension of . It is known that for any fixed admissible indexing φ of there is a countable nonconstructive extension of (relative to φ). The main theorem here shows that there exists an extension of such that for any admissible indexing φ of , is nonconstructive (relative to φ).Thus, in this sense a countable totally nonconstructive extension of .
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