[FOM] inconsistency of P and extreme formalism

Robert Rynasiewicz ryno at lorentz.phl.jhu.edu
Mon Oct 10 12:12:14 EDT 2011

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
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