Higher dimensions

Abstract

The reader must have already noticed that in this book so far, we have only considered functions of the form f : [θ]2 → I or equivalently sequences (Formula presented) of one-place functions. To obtain analogous results about functions defined on higher-dimensional cubes [θ]n. one usually develops some form of stepping-up procedure that lifts a function of the form f : [θ]n → I to a function of the form g : [θ+]n+1 → I. The basic idea seems quite simple. One starts with a coherent sequence eα : α → θ (α < θ+) of one-to-one mappings and wishes to define g : [θ+]n+1 → I as follows: (Formula presented).