[FOM] Choice of new axioms 1
carette at mcmaster.ca
Mon Feb 13 20:00:15 EST 2006
Eray Ozkural wrote:
>I agree with Bauer in that the independence results hint at a
>fundamental relativism in mathematics rather than an
What I find most fascinating here is the contrast with Computer
Science: the Church-Turing thesis has proven itself to be quite
``stable'', and so notions of computations can safely be determined via
any Turing-complete programming language. This gives rise to the very
stable notion of Kolmogorov-Chaitin Complexity, which does not seem to
have a satisfactory counterpart in mathematics (yet!).
This seems to be related to the strong countability assumptions of
Turing machines, as well as some weaker finiteness assumptions (ie
interesting programs terminate). I am eagerly watching the developments
in the ``realizability'' approach to Analysis and other parts of
mathematics, as it appears that quite a bit of mathematics survives, and
is sometimes reborn in quite fascinating new guises.
Has anyone tried to work on Kolmogorov type complexity theory for
mathematical systems which are somehow ``stable''?
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