[SCL] Presentation of the model theory

[james.farrugia at maine.edu]

Some comments regarding Pat's remarks below ...

> pat hayes wrote:
> > BTW, all this makes me think that it might be worth stating the MT
> in
> > 'conventional' terms ( ie without an explicit extension mapping) but
> > being explicit that we are using Aczel's set theory rather than Z_F:
> > what do you think?
> >
> 
> Hi Pat,
> if you are suggesting using non-wellfounded set theory as the basis
> for SCL semantics, I would agree. I suggested this long ago, but it
> seemed that people were reluctant to leave ZF.
> 
> - michael

I think it would be helpful to provide both kinds of presentations,
since my guess is that people are likely to gravitate towards one or 
the other.

Pat's comment suggests to me an option of either/or (or both). 

Would the two presentations "give the same model theory"?  Can it be 
shown that the interpretations and inferences sanctioned by one of the 
presentations are the same as those sanctioned by the other? (Is there
another/better way of showing that two presentations "give the same
model theory"??)

If so, what would be the down side (other than the work involved)
of providing both presentations of the model theory?

Jim