[FOM] Conservation and Ideals

[adame@maths.warwick.ac.uk]

This brings to mind a question I recently wondered about. Namely, is the
Hilbert Basis Theorem provable in PA. Clearly one must do a little bit of
coding, and the full statement (finite generation for all ideals - say for
polynomial rings over Z or the algebraic numbers). However, one could
certainly consider a schema asserting finite generation for all
recursively generated ideals. Are these assertions theorems of PA?

Adam Epstein
Mathematics Institute
University of Warwick
Coventry, UK