[FOM] Re: Goodstein sequence is not provable in PA

Jeff Hirst jlh at cs.appstate.edu
Tue Mar 30 15:29:52 EST 2004


Jhone asked:
>Goodstein sequence is not provable in PA .Is that right? is there a 
>literature on this

Yes and yes.  Early papers on this include:

L. Kirby and J. Paris,  Accessible independence results for Peano Arithmetic,
Bull. London Math. Soc.  14 (1982) , no 4 285--293.  MR0663480

and (independently proven and published slightly later)

E.A. Chicon,   A short proof of two recently discovered independence results
using recursion theoretic methods,  Proc. Amer. Math. Soc.  87 (1983),
no 4  704--706.    MR0687646

Variations on this result and the related hydra results are still 
being published.

Hope this helps...

-Jeff Hirst
Jeff Hirst   jlh at math.appstate.edu
Professor of Mathematics
Appalachian State University, Boone, NC  28608
vox:828-262-2861    fax:828-265-8617

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