[FOM] Re: Candidates for Harvey Friedman's Pi^0_1 formula P(n)

[Timothy Y. Chow]

On Thu, 18 Mar 2004 JoeShipman at aol.com wrote:
> Chow is mistaken.  Homotopy groups of spheres, indeed of any simply
> connected finite complexes, are computable (E.H. Brown, Jr, "Finite
> Computability of Postnikov Complexes", Annl. of Math. 65 (1957), 1-20).

Wow, not only was I mistaken, I was spectacularly wrong!  Fascinating
result.  I wonder, nevertheless, whether there is a homotopy-theoretic
example of some kind available.

Or perhaps some totally different candidate for P(n) would be better?
Word problems and diophantine equations have the necessary undecidability
properties, but it's not so easy to find a family where each instance is
interesting in and of itself.

Tim