FOM: Re: comments on RT2 paper

Stephen G Simpson simpson at
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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