[FOM] 301:Exotic Prefix Theory (correction)
Harvey Friedman
friedman at math.ohio-state.edu
Thu Sep 14 18:09:33 EDT 2006
In 300: Exotic Prefix Theory,
http://www.cs.nyu.edu/pipermail/fom/2006-September/010785.html
I introduced three exotic prefix classes:
Let k >= 1. (forall R containedin [inf]^2k)(therexists S containedin
[inf]^2k)(forall a,b,c,d in [inf]^k)(therexists e,f,g,h in [inf]^k)
(phi(R,S,a,b,c,d,e,f,g,h)).
Let n >> k. (forall R containedin [n]^2k)(therexists S containedin
[n]^2k)(forall a,b,c,d in [n]^k)(therexists e,f,g,h in [n]^k)
(phi(R,S,a,b,c,d,e,f,g,h)).
For all k there exists n such that the following holds. (forall R
containedin [n]^2k)(therexists S containedin [n]^2k)(forall a,b,c,d in
[n]^k)(therexists e,f,g,h in [n]^k) (phi(R,S,a,b,c,d,e,f,g,h)).
Let k >= 1. (forall R containedin [(8k)!]^2k)(therexists S containedin
[(8k)!]^2k)(forall a,b,c,d in [(8k)!]^k)(therexists e,f,g,h in [(8k)!]^k)
(phi(A,B,a,b,c,d,e,f,g,h)).
where phi is a propositional combination of formulas of the form
v < w.
v ~ w.
R(v,w).
S(v,w).
Here v,w are among the variables a,b,c,d,e,f,g,h. Also, ~ denotes order
equivalence.
The correction is in one of the four displayed items. They should read:
v < w.
(x,v) ~ (y,w).
R(v,w).
S(v,w).
Here x,y,v,w are among the variables a,b,c,d,e,f,g,h. Also ~ denotes order
equivalence between the concatenation of x,v, and the concatenation of y,w.
I have no idea if these prefix classes remain exotic if I just use v ~ w.
There is a pdf version on http://www.math.ohio-state.edu/%7Efriedman/
**********************************
I use http://www.math.ohio-state.edu/%7Efriedman/ for downloadable
manuscripts. This is the 301st 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. NOTE: The title of #269 has been corrected from
the original.
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
261. Pi01/nicer 12/5/05 2:26AM
262. Correction/Restatement 12/9/05 10:13AM
263. Pi01/digraphs 1 1/13/06 1:11AM
264. Pi01/digraphs 2 1/27/06 11:34AM
265. Pi01/digraphs 2/more 1/28/06 2:46PM
266. Pi01/digraphs/unifying 2/4/06 5:27AM
267. Pi01/digraphs/progress 2/8/06 2:44AM
268. Finite to Infinite 1 2/22/06 9:01AM
269. Pi01,Pi00/digraphs 2/25/06 3:09AM
270. Finite to Infinite/Restatement 2/25/06 8:25PM
271. Clarification of Smith Article 3/22/06 5:58PM
272. Sigma01/optimal 3/24/06 1:45PM
273: Sigma01/optimal/size 3/28/06 12:57PM
274: Subcubic Graph Numbers 4/1/06 11:23AM
275: Kruskal Theorem/Impredicativity 4/2/06 12:16PM
276: Higman/Kruskal/impredicativity 4/4/06 6:31AM
277: Strict Predicativity 4/5/06 1:58PM
278: Ultra/Strict/Predicativity/Higman 4/8/06 1:33AM
279: Subcubic graph numbers/restated 4/8/06 3:14AN
280: Generating large caridnals/self embedding axioms 5/2/06 4:55AM 281:
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282: Adventures in Pi01 Independence 5/7/06
283: A theory of indiscernibles 5/7/06 6:42PM
284: Godel's Second 5/9/06 10:02AM
285: Godel's Second/more 5/10/06 5:55PM
286: Godel's Second/still more 5/11/06 2:05PM
287: More Pi01 adventures 5/18/06 9:19AM
288: Discrete ordered rings and large cardinals 6/1/06 11:28AM
289: Integer Thresholds in FFF 6/6/06 10:23PM
290: Independently Free Minds/Collectively Random Agents 6/12/06 11:01AM
291: Independently Free Minds/Collectively Random Agents (more) 6/13/06
5:01PM
292: Concept Calculus 1 6/17/06 5:26PM
293: Concept Calculus 2 6/20/06 6:27PM
294: Concept Calculus 3 6/25/06 5:15PM
295: Concept Calculus 4 7/3/06 2:34AM
296: Order Calculus 7/7/06 12:13PM
297: Order Calculus/restatement 7/11/06 12:16PM
298: Concept Calculus 5 7/14/06 5:40AM
299: Order Calculus/simplification 7/23/06 7:38PM
300: Exotic Prefix Theory 9/14/06 7:11AM
Harvey Friedman
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