Recursive analogues of cardinal
and ordinal numbers have been developed by considering only subsets of the natural
numbers and considering only one-to-one partial recursive functions as the maps or
correspondences between sets. The recursive analogue of a cardinal is called a
recursive equivalence type (RET) and that of an ordinal is called a co-ordinal.
Using the RETs and the co-ordinals analogues of Cantor’s number classes are
defined and considered in this paper. The degree of indecomposability of an
RET is seen to determine the set of classical ordinals represented in the
RET’s co-ordinal number class. If the RET is infinite this set of ordinals is
always an initial segment (not necessarily proper) of Cantor’s second number
class.
