The Ordinal Correspondence and Certain Classes of Multiplicative Functions of Two Arguments

The object of this paper is first to establish an important reversible one-to-one correspondence between general multiplicative functions⁽¹⁾ and the ordinal functions.† This correspondence may be referred to as the ordinal correspondence ‡ A remarkable feature of the ordinal correspondence is that it-leaves invariant, the product and the composite of two multiplicative functions, as well as, the inverse of any function.