A Cantor-Bernstein Result for Structured Objects

The notion of a structure system | sets of structured objects that are composed of atomic objects | is introduced by a collection of axioms. By a uniform change of the atomic objects, the relationship, induced by the atomic objects, between the structured objects is preserved, resulting in a notion of isomorphism of sets of structured objects. By de nition, a relation R on such structured sets satis es the Cantor-Bernstein property if A R B and B R A imply that A and B are isomorphic. It is shown that `isomorphic to a subset' does not satisfy the Cantor-Bernstein property. However, a restricted version of this relation does, resulting in an extension of the Cantor-Bernstein proposition for sets of structured objects. Similar results are shown for multisets of structured objects.