FEASIBILITY OF A SET-THEORETIC DATA STRUCTURE. A GENERAL STRUCTURE BASED ON A RECONSTITUTED DEFINITION OF RELATION

Abstract
The paper is motivated by an assumption that many problems dealing with arbitrarily related data can be expedited on a digital computer by a storage structure which allows rapid execution of operations within and between sets of datum names. In order for such a structure to be feasible, two problems must be considered: (1) the structure should be general enough that the sets involved may be unrestricted, thus allowing sets of sets of sets...; sets of ordered pairs, ordered triples...; sets of variable length n-tuples, n-tuples of arbitrary sets; etc.; (2) the set-operations should be general in nature, allowing any of the usual set theory operations between sets as described above, with the assurance that these operations will be executed rapidly. A sufficient condition for the latter is the existence of a well-ordering relation on the union of the participating sets. These problems are resolved in this paper with the introduction of the concept of a 'complex' which has an additional feature of allowing a natural extension of properties of binary relations to properties of general relations.

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