[FOM] Proofs in Computability Theories
Andrej Bauer
andrej.bauer at andrej.com
Mon Sep 21 13:32:54 EDT 2009
The simplest satement in recursion theorem which I do not know how to
prove (purely) constructively is Post's theorem: if both a set and its
complement are c.e. then the set is decidable. As far as I can tell,
the proof requires Markov principle (or something slightly weaker).
Markov principle is a particular instance of the general classical
principle Reductio ad Absurdum (not not p implies p).
With kind regards,
Andrej
On Mon, Sep 21, 2009 at 1:04 AM, Aatu Koskensilta
<Aatu.Koskensilta at uta.fi> wrote:
>For non-constructive theorems in recursion theory we need look elsewhere,
> ranging from the classically trivial result that a finite set is
> decidable to more interesting stuff about immune sets etc.
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