Let N be the set of all nonnegative integers. The following are equivalent. We are now ready to state the first independence result. We conclude by stating the following sharper, but equivalent, forms of Propositions 2.2 and 2.4. Regressive functions on partial orderings.
E is called the basis for f.
As in section 1, we define the degree of f as the number of elements in its basis. We say that g is an almost restriction of f if and only if every proper restriction of g is a restriction of f. 1 is a restriction of f. 1 is a m-restriction of f. These results do not hold for degree 1.