[FOM] 261:Pi01/nicer
Harvey Friedman
friedman at math.ohio-state.edu
Mon Dec 5 02:26:51 EST 2005
I have made the Pi01 independent statement nicer, and put up the new version
at
http://www.math.ohio-state.edu/%7Efriedman/
under downloadable manuscripts, manuscript number 49. I have retained the
two previous versions. This latest is dated December 4, 2005.
>From posting #260, the December 3 version (see website), we had
OLD THEOREM 1.4. For all k,n >= 1, every strictly dominating order invariant
R containedin [1,n]2k has an antichain A such that flog R[A\2^(8k)!-1]
contains flog A'.
OLD PROPOSITION A. For all k,n >= 1, every strictly dominating order
invariant R containedin [1,n]2k has an antichain A such that flog
RRRR[A\2^(8k)!-1] contains flog RRR[A'].
We now have
NEW THEOREM A(1,0). For all k,n >= 1 and t >= (8k)!, every strictly
dominating order invariant R containedin [1,n]2k has an antichain A such
that flog_t+1 R[A\{t}k] = flog_t+1 A'.
NEW PROPOSITION A(4,3). For all k,n >= 1 and t >= (8k)!, every strictly
dominating order invariant R containedin [1,n]2k has an antichain A such
that flog_t+1 RRRR[A\{t}k] = flog_t+1 RRR[A'].
*************************************
I use http://www.math.ohio-state.edu/%7Efriedman/ for downloadable
manuscripts. This is the 259th in a series of self contained numbered
postings to FOM covering a wide range of topics in f.o.m. The list of
previous numbered postings #1-249 can be found at
http://www.cs.nyu.edu/pipermail/fom/2005-June/008999.html in the FOM
archives, 6/15/05, 9:18PM.
250. Extreme Cardinals/Pi01 7/31/05 8:34PM
251. Embedding Axioms 8/1/05 10:40AM
252. Pi01 Revisited 10/25/05 10:35PM
253. Pi01 Progress 10/26/05 6:32AM
254. Pi01 Progress/more 11/10/05 4:37AM
255. Controlling Pi01 11/12 5:10PM
256. NAME:finite inclusion theory 11/21/05 2:34AM
257. FIT/more 11/22/05 5:34AM
258. Pi01/Simplification/Restatement 11/27/05 2:12AM
259. Pi01 pointer 11/30/05 10:36AM
260. Pi01/simplification 12/3/05 3:11PM
Harvey Friedman
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