[FOM] axiomatisations of PA

[UCKELMAN, SARA L.]

Hi all,
I've got a 3rd year philosophy undergrad working on notions of 
descriptive completeness, and he keeps turning up to my office hours 
with questions that I can't _quite_ answer simply because I don't have 
the right breadth.

Today he was asking about the variety of axiomatisations of PA, some of 
which use the notion of "natural number" directly in the axioms, while 
others (e.g., the one used by Goldstern & Judah) have axioms governing 
each of the mathematical functions + induction.

Has anyone ever written on the development of axiomatisations of PA, 
from a moderately historical, rather than mathematical, perspective? 
I'd love to be able to give him something that traces who developed 
which axiomatisations and when and why, keeping in mind that he's not a 
hard-core mathematician.  This strikes me as the sort of thing that 
surely someone has written a PhD thesis on sometime (and if not, someone 
should!).

Cheers,
-Sara


-- 
Dr. Sara L. Uckelman
Department of Philosophy
Durham University
http://community.dur.ac.uk/s.l.uckelman/

The Dictionary of Medieval Names from European Sources
http://dmnes.org/