Abstract
Axioms are given for an equivalence relation defined in a product set, such that a commutative group structure can be introduced in the set of equivalence classes. Different group structures in the same product set, obtained by this construction, are all naturally isomorphic. If the group is Archimedean ordered, an isomorphism into the ordered additive reals leads to interval scale measurement. Similar theorems result from axioms stated symmetrically for several interlocking equivalence relations on a single set. Group structures are constructed on each set of equivalence classes, and a “global” group structure is obtained on the whole set, modulo the intersection of the equivalence relations.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
