Two relations R and R' are said to be ordinally similar, if a one-one relation holds between the members of the two fields of R and R', such that if x and y are any two members of the field of R, such that x has the relation R to y, and if x' and y are the correlates in the field of R' of x and y, then in all such cases x has the relation R' to y', and conversely, interchanging the dashes on the letters, i.e.
Also, two relations need not be serial in order to be ordinally similar; but if one is serial, so is the other.
The relation-number of a relation is the class whose members are all those relations which are ordinally similar to it.
How would you define ordinally? Add your definition here.