Low₅ Boolean subalgebras and computable copies

Journal of Symbolic Logic 76 (3):1061 - 1074 (2011)

Abstract
It is known that the spectrum of a Boolean algebra cannot contain a low₄ degree unless it also contains the degree 0; it remains open whether the same holds for low₅ degrees. We address the question differently, by considering Boolean subalgebras of the computable atomless Boolean algebra B. For such subalgebras A, we show that it is possible for the spectrum of the unary relation A on B to contain a low₅ degree without containing 0
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DOI 10.2178/jsl/1309952534
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Computable Boolean Algebras.Julia F. Knight & Michael Stob - 2000 - Journal of Symbolic Logic 65 (4):1605-1623.
Recursive Isomorphism Types of Recursive Boolean Algebras.J. B. Remmel - 1981 - Journal of Symbolic Logic 46 (3):572-594.

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