FOM: Re: comments on RT2 paper
Stephen G Simpson
simpson at math.psu.edu
Thu Oct 22 16:53:15 EDT 1998
Peter Cholak writes:
> Thanks for your interest in our paper. Thanks for pointing out our
> error. It along with any mathematical errors you or anyone else
> find will be corrected in the next version of the paper.
Dear Peter,
Your paper on the reverse mathematics of Ramsey's theorem is indeed
very impressive.
One further comment:
On page 4 of your paper you state corollary 11.5: RCA_0 +
RT(2,<infinity) proves B Sigma_3. You say that this is an improvement
of a 1996 result of Mytilinaios and Slaman. But actually my former
Ph. D. student Jeff Hirst proved in his 1987 Ph. D. thesis that
RT(2,<infinity) implies B Pi^0_2 and the totality of the Ackermann
function, over RCA_0. Should this be cited? In fact, B Pi^0_2 is
equivalent to B Sigma_3, isn't it? (Unless I'm confused.)
I notice that Hirst's thesis is in your list of references, but I
haven't yet discovered where you actually refer to it.
Best regards,
-- Steve
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