Computable ideals in \(I\)-algebras (Q619312)

An \(I\)-algebra is a structure of the form \((B,I_1,\dots,I_k)\) where the \(I_j\) are ideals of the Boolean algebra \(B\). The structure is called computable in the obvious way. The author gives algebraic/syntactic descriptions of relatively intrinsically computable (in the sense of Ash-Nerode) ideals in \(I\)-algebras, and of intrinsically computable ideals in the case of two distinguished ideals. This should be compared with the author's earlier work on computably categorical \(I\)-algebras [Algebra Logika 43, No. 5, 511--550 (2004; Zbl 1096.03042)].