FOM: Re: comments on RT2 paper

Peter Cholak cholak at
Thu Oct 22 17:53:10 EDT 1998

Steve and Jeff,

Hirst's thesis is cited on page 51 line -5. 
I actually do not have a copy of Jeff's thesis.  Perhaps someone might
send me a copy, if that is possible. 

You are correct that B Pi^0_2 is equivalent to B Sigma_3 and hence
Corollary 11.5 is due to Hirst.  I am sure none of us were aware of Jeff's
result -- I certainly was not.  Anyway clearly this will be corrected and
more carefully noted in the next version.

I am very interested in Jeff's result that RT(2,<infinity) implies the
totality of the Ackermann function, over RCA_0.  I would like to see it's
proof.  Could Jeff's result be improved to RT(2,2)? (See Question 13.2 in
our paper.)

For those interested I posted several copies of our paper on the web at

	      Peter Cholak <Peter.Cholak.1 at>
Department of Mathematics	|	Phone: (219) 631-6507
University of Notre Dame	|	Fax:   (219) 631-6579
Notre Dame, Indiana 46556-5683	|	Office 223 CCMB

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