Mathematics with the potential infinite

[Timothy Y. Chow]

Matthias wrote:

> for several years I have been engaged in developing mathematics solely 
> with the concept of the potential infinity. Two publications of mine are 
> now available.

This is interesting.  The topic of potential infinity has come up on FOM 
before a few times, e.g., in March 2015---

https://cs.nyu.edu/pipermail/fom/2015-March/

---and in July 2020, when you made a few comments:

https://cs.nyu.edu/pipermail/fom/2020-July/

One question I have in general for any account of potential infinity is 
this: Can you give examples of statements that are provable using "actual 
infinities" but that are not provable using "potential infinity" only? 
(Here, I exclude statements that don't even make sense unless you assume 
actual infinities.)  As a specific test case of interest, can you prove 
"PA is consistent" using only only potential infinity?

Tim