**Authors:** Richard Beigel, William Gasarch, and Louise Hay

**Abstract:**
Let *A* be any nonrecursive set. We define a hierarchy of sets
(and a corresponding hierarchy of degrees) that are reducible to
*A* based on bounding the number of queries to *A* that an
oracle machine can make. When *A* is the halting problem
*K* our hierarchy of sets interleaves with the difference
hierarchy on the r.e. sets in a logarithmic way; this follows from a
tradeoff between the number of parallel queries and the number of
serial queries needed to compute a function with oracle *K*.