# [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.

**********************************

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:
Linear Self Embedding Axioms  5/5/06  2:32AM
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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