Low5 Boolean subalgebras and computable copies

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.