The transfinite recursion theorem is proved, and the usual operations on ordinals are defined. It is proved that the natural order on the ordinals is a well-ordering. The book then turns to the development of the theory of cardinal number. Cardinals are defined as equivalence classes of sets under the relation of being the same size, defined in the familiar way. Addition and multiplication of infinite cardinals are shown to have the familiar properties we expect in much the same way as in the usual set theory.
Exponentiation presents a different picture.
The usual way of defining exponentiation of cardinals is not stratified.