Geodesic
Computable numberings of the class of Boolean algebras with distinguished endomorphisms
Algebra i logika, Tome 52 (2013) no. 5, pp. 535-552

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We deal with computable Boolean algebras having a fixed finite number $\lambda$ of distinguished endomorphisms (briefly, $E_\lambda$-algebras). It is shown that the index set of $E_\lambda$-algebras is $\Pi^0_\2$-complete. It is proved that the class of all computable $E_\lambda$-algebras has a $\Delta^0_3$-computable numbering but does not have a $\Delta^0_2$-computable numbering, up to computable isomorphism. Also for the class of all computable $E_\lambda$-algebras, we explore whether there exist hyperarithmetical Friedberg numberings, up to $\Delta^0_\alpha$-computable isomorphism.
Keywords: computable Boolean algebra with distinguished endomorphisms, computable numbering, Friedberg numbering, index set, isomorphism problem. 
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     author = {N. A. Bazhenov},
     title = {Computable numberings of the class of {Boolean} algebras with distinguished endomorphisms},
     journal = {Algebra i logika},
     pages = {535--552},
     publisher = {mathdoc},
     volume = {52},
     number = {5},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2013_52_5_a0/}
}
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N. A. Bazhenov. Computable numberings of the class of Boolean algebras with distinguished endomorphisms. Algebra i logika, Tome 52 (2013) no. 5, pp. 535-552. http://geodesic.mathdoc.fr/item/AL_2013_52_5_a0/