On 3/19/2013 10:17 AM, Ross A. Finlayson wrote: >> >> And yes, forcing is unobjectionable when you redefine truth. >> >> But, no one told anyone. > > If you might elucidate on that, it may help to establish the context a > bit more firmly to the gallery. >
It is not a mathematical issue.
Forcing changes what it means for something to be true in mathematics if the outcome is to define truth in terms of "truth persistence under forcing".
Tarski-based semantics is replaced by the kind of thing that is discussed in the book by Langholm.
To change the classical problem is not the same as solving the classical problem.
For example, suppose it to be true that partial systems are not diagonalizable.
I make this guess simply because a presumption of the diagonal argument is a presumption that "all" of the objects have been given a locus in the list.
Non-diagonalizability is a "truth" of partial systems.