[FOM] Re: Absoluteness of Clay prize problems

[Aatu Koskensilta]

On Aug 23, 2004, at 10:11 PM, Dmytro Taranovsky wrote:

> Also, regarding the Continuum Hypothesis, the problem is an important 
> basic
> mathematical (or, some would say, metamathematical) problem in its own 
> right,
> so study related to CH is important even if it has no known (non 
> Sigma-0-1)
> Pi-0-1 or commercial applications.

CH has no arithmetical consequences, .i.e. ZFC + CH is conservative 
over ZFC for
arithmetical statements. This also holds for Sigma^1_2 and Pi^1_2 
statements.

-- 
Aatu Koskensilta (aatu.koskensilta at xortec.fi)

"Wovon man nicht sprechen kann, daruber muss man schweigen"
  - Ludwig Wittgenstein, Tractatus Logico-Philosophicus