[FOM] inconsistency of P and extreme formalism

[Robert Rynasiewicz]

On Sat 08.10.11, at 10:17 PM, Brian White wrote:

> The notions of formula, proof, consistency can be defined
> in systems that are much weaker than P.  
> 

For my edification, what is the weakest system needed?  (N.B. I'm interested in a robust sense of consistency, viz., that a theory is consistent iff it is not the case that some sentence and its negation are both theorems, not the weaker sense that not everything is a derivable [as is the case, e.g., with lambda calculus].) 

Robert Rynasiewicz
-------------- next part --------------
An HTML attachment was scrubbed...
URL: </pipermail/fom/attachments/20111010/4fd7e248/attachment.html>