[FOM] Arithmetic-free theory of formal systems?

[Matthew Frank]

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?

> that directly formalizes the concepts of "symbol,"
> "concatenation," etc. without reference to arithmetic concepts.

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