[FOM] Arithmetic-free theory of formal systems?

[Steven Ericsson Zenith]

On Mon, 17 May 2004, Timothy Y. Chow wrote:

> is there a way of developing a theory of formal systems without
> any reference to arithmetic?

To which Matthew Frank <mfrank at math.uchicago.edu> replied ...

> One good example is:  Jeroslow, R. G., "Redundancies in the
> Hilbert-Bernays derivability conditions for Gdel's second incompleteness
> theorem", J. Symbolic Logic 38 (1973), 359-367.

> There's also Smullyan's "Theory of Formal Systems", though I found it
> harder to read.  --Matt

Timothy might also consider a review of the Charles Sander Peirce volume "Exact Logic" - 
volume 4 of the CSP Collected Papers as I recall.

Steven