A notion of helping and pseudo-complementation in lattices of honest subrecursive classes

A notion of one computable function (not) helping the computation of another is defined in terms of the lattices of honest subrecursive classes. It is said that two honest computable functions do not help each other´s computation if the intersection (meet) of the subrecursive classes which they generate is the zero subrecursive class; that is, two functions do not help each other´s computation if they have trivial information content in common. One honest subrecursive class is said to be the pseudo-complement of another if it is the maximum class which has trivial information content in common with the other. A technical characterization is given of those honest subrecursive classes for which there are non-zero honest subrecursive classes with trivial information content in common with them. Further, it is shown that for every non-zero honest subrecursive class there is an effective, increasing sequence of honest subrecursive classes which have trivial information content in common with it, and this sequence is cofinal upwards with the set of all honest subrecursive classes which have trivial information content in common with it. Although there is always an upper bound to the set of classes which can have trivial information content in common with it, there may or may not be a maximum class with this property.