[FOM] foundational philosophies and core mathematics

[Harvey Friedman]

On 2/13/06 3:32 AM, "Nik Weaver" <nweaver at math.wustl.edu> wrote:

>  I want to
> make the point that the predicative conception of mathematical
> reality is in fact in remarkably exact accord with normal
> mathematical practice, much better than for any alternative
> foundational stance of which I am aware.

Do you have any significant range of examples of what you call "normal
mathematics" that is covered under "predicativism" but not under ACA0?

Do you have any significant range of examples of arithmetical theorems in
what you call "normal mathematics" that aren't provable in PA? Aren't
provable in EFA = exponential function arithmetic?

>Moreover, virtually all of
> core mathematics can be made predicative with only minor
> modifications, whereas vast regions of set-theoretic pathology
> simply disappear.  I'll say more about this in my next message.
> 

Can "virtually all of core mathematics" be done in ACA0 "with only minor
modifications"? In RCA0?

Harvey Friedman