Complexity of some natural problems on the class of computable I-algebras

Abstract

We study computable Boolean algebras with distinguished ideals (I-algebras for short). We prove that the isomorphism problem for computable I-algebras is Σ 1 1 -complete and show that the computable isomorphism problem and the computable categoricity problem for computable I-algebras are Σ 0 3 -complete.