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.
"Low5 Boolean subalgebras and computable copies." J. Symbolic Logic 76 (3) 1061 - 1074, September 2011. https://doi.org/10.2178/jsl/1309952534