Michael Machtey

TL;DR: A strong connection is established between the structural and the looking back techniques for manipulating the relative complexity of computable functions and exploring the nature of subrecursive reducibilities.

TL;DR: A classification of all the computable functions is given in terms of subrecursive programming languages and it is shown that any countable partial ordering can be embedded in the dishonest classes, and that the dishonestclasses are dense in the honest classes.

TL;DR: It is shown that the honest subrecursive classes are dense under the partial ordering of set inclusion and there exists a pair of incomparable honest sub Recursion classes such that the greatest lower bound of the pair is the smaller of the first two classes and the least upper bound is the larger of thefirst two classes.

TL;DR: It is shown that the honest subrecursive classes are a distributive lattice under the partial ordering of set inclusion, and every honest sub Recursion class is the greatest lower bound of two setwise incomparable honest sub recursion classes.