No subject

Robert I. Soare soare at
Thu Aug 5 17:06:49 EDT 1999

DATE:   Thursday, August 5, 1999
TO:     FOM (Foundations of Mathematics):   fom at
FROM:  	Robert Soare, The University of Chicago
RE:    (1) A CURIOUS TRANSLATION; (2) The Low Basis Theorem


I told fom three days ago that I came to fom NOT to debate, but
just to have corrected ERRORS and MISIMPRESSIONS by Mr. Simpson
in his summary (FOM June 21 1999) of the Boulder meeting.


Regarding communication with Mr. Simpson and his public posting of
information, the NEXT TWO items taken together are revealing and
require no explanation from me.


>   Date: Wed, 4 Aug 1999 16:08:36 -0700
>   To: fom at
>   From: CTSteel <steelnet at>
>   Subject: FOM: Sigma_1^1-AC error
>   The errors in Bob Soare's statements about Sigma_1^1-AC versus Sigma_1^1-DC
>   are due to me (and perhaps also Harrington), not to Soare. Harvey proved that
>   Sigma_1^1-AC does not imply Sigma_1^1-DC. I confused this with some other
>   work, and this led to Soare's mis-attribution. Bob was careful enough to
>   ask me about it several times, so the fault is all mine.
>   Harrington did prove Delta_1^1-CA does not imply Sigma_1^1-AC. I believe his
>   proof had a priority argument in it, although to my mind its most ingenious
>   feature was its use of Sacks' "shiny little box" technique, which is based
>   on Kleene's Recursion Theorem.
>   John Steel

ITEM 1B:  Mr. SIMPSON REPORTED this event as:

>   From: Stephen G Simpson <simpson at>
>   Date: Thu, 5 Aug 1999 06:49:14 -0400 (EDT)
>   To: comp-thy at, fom at
>   Subject: FOM: Soare on FOM
>   Organization: Department of Mathematics, Pennsylvania State University
>   Dear FOM and COMP-THY subscribers,
>   ... 
>    "Also on the FOM list,
>   John Steel and I are in the process of correcting some of Soare's
>   false claims, and Soare has partially backed away from some of them."
>	...


John Steel was not involved in the discussion of any OTHER claim in
Soare's FOM Aug. 3 paper, so Simpson's reference could only have been
to THIS incident.

The reader might ask himself, "Do you think that this was this FAIRLY
and ACCURATELY reported by the Moderator?"  If so, fine!  If not, are
there any OTHER items routinely announced, reviewed, claimed,
proposed, and put forward BY THE MODERATOR which may in fact be
SLANTED just a teeny weeny little bit?  This is just an abstract


About using a PRIORITY ARGUMENT or the LOW BASIS THEOREM in a theorem


>    Soare claims on his web page and in FOM 2 Aug 1999 12:54:07 that
>       > If one specifically desires applications of the priority method
>       > to Reverse Mathematics, then Mytilinaios and Slaman used a
>       > priority argument in their Reverse Mathematics paper, "On a
>       > question of Brown and Simpson," and solved a problem posed by
>       > Brown and Simpson in 1993.
>      But this claim by Soare is incorrect.  I happen to be familiar with
>      this area!  The result in question is that BCT-II does not imply
>      RCA_0^+.  The Mytilinaios/Slaman proof of this result uses the low
>      basis theorem but does not use a priority argument.  (With regard
>      to the low basis theorem, see below.)  There is a priority argument
>      in the Mytilinaios/Slaman paper, but it doesn't address reverse
>      mathematics.


However, SLAMAN, the COAUTHOR, wrote on Aug. 5 in private email to Soare,
that Simpson is WRONG.

>   Date: Thu, 5 Aug 1999 13:16:02 -0700 (PDT)
>   From: "Theodore A. Slaman" <slaman at>
>   To: "Robert I. Soare" <soare at>
>   Subject: Low basis theorem
>   "Simpson wrote to me separately about the FOM discussion.  I pointed
>   out to him that Mytilinaios-Slaman does NOT USE the low basis theorem,
>   to which he agreed."
>               ...
>   "Even so, I would say that M-S APPLIED the PRIORITY  METHOD in proving
>   the theorem."


It is TOUCHING to see to what great lengths Simpson will go with his
"ETHNIC CLEANSING" of the Holy Grail of REVERSE MATHEMATICS to keep it
pure and to protect from the TAINT of "PRIORITY ARGUMENTS."


Well, we are making some PROGRESS.  We have ONE RETRACTION from
MR. SIMPSON for a mathematical error or misstatement, but not yet a FULL
APOLOGY on FOM as I gave yesterday.  Maybe we will have that tomorrow.
There is also the matter of the other questions have I raised in the last
few days.


FINALE:  MR. SIMPSON wrote to FOM on what MR. FRIEDMAN had written
	 to FOM earlier.  I want to express my full support!!

>  Date: Thu, 10 Jun 1999 14:12:35 -0400 (EDT)
>  From: Stephen G Simpson <simpson at>
>  Subject: FOM: awe; an unusual recursion theory meeting
>  Harvey Friedman 8 Jun 1999 11:52:08
>   > As you notice, I feel obliged to defend the greatness of the f.o.m.
>   > enterprise, and stand in awe of its achievements and possibilities,
>   > as I stand on the shoulders of giants such as Aristotle, Frege and
>   > Godel.  Apparently not all subscribers share this awe.
>  Harvey, I agree with you that some FOM subscribers do not have
>  appropriate reverence and respect for the achievements and
>  possibilities of the f.o.m. enterprise.


R. SOARE:  SHAME ON YOU!  FOM subscribers, not to "HAVE
   APPROPRIATE REVERENCE and RESPECT for the achievements and
   possibilities of the f.o.m. enterprise."

		I certainly do!!

QUESTION.  OK. But WHY do they have to stand on the SHOULDERS of so
	   many other people?  

ANSWER.	   YOU can answer this!

Robert I. Soare
Paul Snowden Russell 
Distinguished Service Professor
    of Mathematics and Computer Science			
Department of Mathematics 	     PHONE: (773) 702-6029, Secty: 702-7100 
The University of Chicago            FAX:   (773) 702-9787
5734 University Avenue		     E-MAIL:	soare at
Chicago, IL 60637-1546	USA  	     WEB:

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