[FOM] extramathematical notions and the CH
Aatu.Koskensilta at uta.fi
Tue Feb 5 18:30:34 EST 2013
Quoting joeshipman at aol.com:
> This also answers Aatu Koskensilta's concern, because CH and V=L and
> similar non-absolute axioms cannot decide any arithmetical
> statements that were not
> already decidable in ZF.
Sure, but "algorithm A provides an approximation to the constant C"
is not an arithmetical statement unless C has an arithmetical
description. The (hypothetical) situation I had in mind was where C is
defined in terms of e.g. sets of reals or other more exotic
mathematical structures, and to prove the correctness of this or that
(computable or at least arithmetical) approximation we must use e.g.
CH or other "non-absolute" principles. This possibility is not ruled
out by the usual absoluteness results.
Aatu Koskensilta (aatu.koskensilta at uta.fi)
"Wovon man nicht sprechen kann, darüber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
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