Operating on the universe (Q1095900)

In spite of the fact that the ZF universe is not well-ordered, it behaves in some respects like the ordinals. It is possible to define on it the usual operations of addition, multiplication and exponentiation, which enjoy similar properties as those on the ordinals. Further, when restricted to the ordinals, the operations coincide, so that ordinal arithmetic can be regarded as an immediate consequence of the universe arithmetic. But more than that: the rank which retracts the universe of sets onto the ordinals is a homomorphism between the universe arithmetical structure \(<V,+,.,\exp >\) and the ordinal arithmetical structure \(<Ord,+,.,\exp >\).