[FOM] reading the bible with Bill: hermeneutics with Gabriel Correctiomn

[William Tait]

In my earlier posting today, I wrote

> free variables over choice sequences (say of natural numbers) have  
> to be understood as a notation indicating that natural number- 
> valued functions of these variables must be locally uniformly  
> continuous (or, equivalently, their unsecured sequences must be  
> well-founded).

This was not what I meant, of course. Rather, functions f: N^N -->N^N  
regarded as being defined on free choice sequences  are to be  
understood as locally uniformly continuous or, equivalently, the  
unsecured sequences of g: N^N x N --> N, defined by g(a, n) = f(a) 
(n), are to be well-founded. (I was referring to something that I  
wrote in an earlier reply to Gabriel.)

Bill Tait