The Honest Subrecursive Classes Are a Lattice

The relation of honest subrecursive classes to the computational complexity of the functions they contain is reviewed. It is shown that the honest subrecursive classes are a distributive lattice under the partial ordering of set inclusion. The meet and join operations of the lattice are effective, and every honest subrecursive class is the greatest lower bound of two setwise incomparable honest subrecursive classes.