[FOM] axiomatisations of PA

[Lukasz T. Stepien]

 Dear Sara L. Uckelman 

   For example, there in the book: "Giuseppe Peano between Mathematics
and Logic. Proceeding of the International Conference in honour of
Giuseppe Peano on the 150th anniversary of his birth and the centennial
of the Formulario Mathematico, Turin (Italy), October 2-3, 2008", Fulvia
Skof - Editor, (Springer-Verlag Italia 2011), in the chapter "Peano and
the Foundations of Arithmetic" written by Gabriele Lolli, the axioms
used by Peano have been presented. Of course, this solves your issue
only partially, however, I hope that this can help you.   

                                                                        
                                                  Regards, 

                                                                        
                                            Lukasz T. Stepien

---

Lukasz T. Stepien

The Pedagogical University of Cracow
Institute of Computer Science,
ul. Podchorazych 2
30-084 Krakow
Poland

tel. +48 12 662-78-54, +48 12 662-78-44

The URL  http://www.ltstepien.up.krakow.pl

On 2019-12-06 15:11, UCKELMAN, SARA L. wrote:

> 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
-------------- next part --------------
An HTML attachment was scrubbed...
URL: </pipermail/fom/attachments/20191206/300c09bd/attachment.html>