Vol. 26, No. 3, 1968

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Full co-ordinals of RETs

Alfred Berry Manaster

Vol. 26 (1968), No. 3, 547–553

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.

Mathematical Subject Classification
Primary: 02.70
Received: 23 May 1967
Published: 1 September 1968
Alfred Berry Manaster