[FOM]: Independece without Forcing

[Roger Bishop Jones]

Todd Eisworth wrote:

> >When I originally posed the question, I had in mind
> > speculating about the existence of "mathematical" statements
> > P such that ZFC + V=L + P is consistent but not in a
> > "standard" (read transitive?) version of L.

Harvey Friedman wrote:

> I don't quite know what you mean by this.

I would guess that "not Con(ZFC + V=L)" would be
an example of something "consistent but not in a
standard (read transitive?) version of L", and
Todd is looking for something "mathematical" which
has the same status.

"Consistent" presumably should be read
"consistent with ZFC + V=L".

"standard (read transitive?) version of L"
presumably means
"standard model of ZFC + V=L" (and these are
presumably the well-founded models).

This is an odd thing to ask for, but it is equivalent
to asking for the negation of something true but
unprovable in ZFC + V=L,
i.e. the negation of a "mathematical" incompleteness
in ZFC + V=L.

Roger Jones