[FOM] strong hypotheses and the theory of N

[rgheck]

On 03/15/2010 08:00 PM, joeshipman at aol.com wrote:
> What more can you [Harvey] say about what "natural" means...
>
> A related question: is there a natural way to represent the
> "arithmetical content" of ZF by arithmetical axioms; in other words, a
> natural decidable set of arithmetical statements which have the same
> arithmetical consequences as ZF?
>
>    
Well, here the meaning of "natural" will be really critical, since we 
can easily find a decidable set of arithmetical statements that has the 
same arithmetical consequences as ZF. Proof: The set of arithmetical 
consequences of ZF is RE. Now apply Craig's trick.

Richard