Torkel Franzen wrote:
> Jan Hidders <jan.hidders_at_REMOVETHIS.pandora.be> writes:
>
>>Note that Mikito was asking about the case where you also had PA in your
>>logic, so the structure also includes the constant 0 and the succesor
>>function.
>
> Then we haven't yet arrived at a precise formulation of the matter
> at issue. Your earlier formulation was
>
> In a structure with the two binary relations R and S. The formula should
> be true for precisely those structures in which S is the transitive
> closure of R.
>
> but from your comments above, this is not in fact what you had in
> mind.
I immedeately admit that my formulation was sloppy here but it seemed
obvious to me that if we are talking about a logic including PA then the
signature also contains the functions that are necessary for doing PA.
By now I think you have enough information to know what the exact
problem is. So for the sake of clarity: the structure consists of D, R,
S, 0 and succ, and nothing else.
Received on Sat May 21 2005 - 05:39:33 CDT
