Geodesic
Constructivizability of the Boolean algebra $\mathfrak B(\omega)$ with a~distinguished automorphism
Algebra i logika, Tome 51 (2012) no. 5, pp. 579-607.

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A constructivizability criterion for the Boolean algebra $\mathfrak B(\omega)$ with a distinguished ideal is given. As a consequence of the criterion, combined with a result due to I. Kalimullin, B. Khoussainov, and A. Melnikov, we construct a Boolean algebra with a distinguished ideal whose degree spectrum contains every nonzero Turing $\Delta^0_2$-degree but does not contain $0$.
Keywords: Boolean algebra with distinguished automorphism, constructivizability, degree spectra of structures. 
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N. A. Bazhenov; R. R. Tukhbatullina. Constructivizability of the Boolean algebra $\mathfrak B(\omega)$ with a~distinguished automorphism. Algebra i logika, Tome 51 (2012) no. 5, pp. 579-607. http://geodesic.mathdoc.fr/item/AL_2012_51_5_a1/

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