[FOM] Independence without forcing

[Todd.Eisworth@uni.edu]

[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."

I am giving 'real mathematics' a loose interpretation --- almost 
anything except a Godel sentence counts. The position as stated does 
not claim that the quoted axioms are true, only that everything of 
interest is decided by them.

Is the position a valid one or not? Assuming it is not, is a 
refutation in the realm of 'science-fiction', or will I discover the 
answer sometime in the coming week while I'm reading more about 
Boolean relation theory?


Best,

Todd