[FOM] Enumerations

Studtmann, Paul pastudtmann at davidson.edu
Tue Apr 5 11:02:43 EDT 2005

For any n, it is possible to enumerate all the n-tuples.  I have seen
formulas that for any x, will give the x-th member of an enumeration of
pairs.  I am wondering, however, whether anyone knows of a definition of a
function that will take any three numbers, x y and z, and yield the z-th
member of the y-th x-tuple in an enumeration of the x-tuples.  Presumably,
such a function is definable within Robinson's Arithmetic, since there is an
effective procedure for computing such a function.  It is not obvious to me,
however, whether there is some natural way of defining such a function.

Paul Studtmann

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