Every Low 2 Boolean Algebra has a Recursive Copy

Abstract

The degree of a structure sv is the Turing degree of its open diagram D(vl) , coded as a subset of co. Implicit in the definition is a particular presentation of the structure; the degree is not an isomorphism invariant. We prove that if a Boolean algebra v has a copy of low 2 degree, then there is a recursive Boolean algebra -7 which is isomorphic to v . This builds on work of Downey and Jockusch, who proved the analogous result starting with a low 1 Boolean algebra.