[FOM] Re: Absoluteness of Clay prize problems
Aatu Koskensilta
aatu.koskensilta at xortec.fi
Tue Aug 24 15:19:40 EDT 2004
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
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