[FOM] Independence without forcing

[Roger Bishop Jones]

On Sunday 13 July 2003 10:59 am, Todd.Eisworth at uni.edu wrote:
> [Reply to Friedman]
>
> In the archives, I found a post by Gaifman where he asks about
> V=L and "hard core independence proofs". If I interpret things
> correctly, he and I are asking nearly the same thing.  Here's
> a more precise formulation.
>
> Consider the following position:
>
> "All statements of 'real mathematics' are decided in the axiom
> system ZF + V=L + there are no inaccessible cardinals; all
> other statements are metamathematical."

This seems in pretty stark contrast with the recent work
of Woodin (at least, as presented by Dehornoy).

Woodin's work seems to suppose that any credible axiom
used in settling questions left open by ZFC should be
compatible with (all?) large cardinal axioms.
A major aim of this work is to show that CH is false
which would of course also show the falsity of V=L.

It seems particularly odd that V=L should figure
so prominently when you don't even want to claim
that it is true!

Are you or Gaifman able to marshall any arguments in
support of your position?

Roger Jones