The degree spectra of definable relations on Boolean algebras

We study some questions concerning the structure of the spectra of the sets of atoms and atomless elements in a computable Boolean algebra. We prove that if the spectrum of the set of atoms contains a 1-low degree then it contains a computable degree. We show also that in a computable Boolean algebra of characteristic $(1,1,0)$ whose set of atoms is computable the spectrum of the atomless ideal consists of all $\Pi_2^0$ degrees.