ABSTRACT
We return to the tree of numbers sketched in Chapter 0, and make precise some of the notions described there. Greek letters tx,p ,y ,... will denote arbitrary ordinal numbers.
For each ordinal a we define a set Ma of numbers by setting x = {x1, | x*} in Ma if all the x1, and x* are in the union of all the Mf for ft < a. Then we set Oa = (J and N , = M , \ Oa. Then in the terminology of Chapter 0
(to which we shall adhere): is the set of numbers bom on or before a (Made numbers),
Nt is the set of numbers bom first on day a (New numbers), and Oa is the set of numbers bom before day a (Old numbers). Now each x e Nt defines a Dedekind section L, R of Oa, if we set
^ = { y e O jy < x}, and R = {y e Oa | y > x}.
