[FOM] From theorems of infinity to axioms of infinity

[Nik Weaver]

Tim Chow wrote:

> This argument, though, isn't sharp enough to justify a specific version 
> of set theory, and there's still plenty of room to argue that this or 
> that umbrella is too large or too small.

Tim,

My paper "Analysis in J_2" (arXiv:math/0509245) might be of interest.
I show how core mathematics, particularly abstract analysis, can be
developed within Jensen's J_2.  This is a set theoretic structure,
but a very concrete one, I would say just as concrete as the natural
numbers.

So if you're wedded to the language of set theory I don't object.
Personally I feel that if one is working at this level of specificity
then third order arithmetic is a little nicer.

Nik