[FOM] Conservation and Ideals

adame@maths.warwick.ac.uk adame at maths.warwick.ac.uk
Tue Aug 9 13:05:21 EDT 2005

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

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