[FOM] 536: Pi01 Progress

[Harvey Friedman]

We have a very polished new version of #82 at
https://u.osu.edu/friedman.8/foundational-adventures/downloadable-manuscripts/

This features many more better organized variants of implicitly Pi01
for Con(SRP), using a bit different notation, with the interval
Q[-n,n] and "critical point" 0, instead of Q[0,n] and "critical point"
1.

Also it has the recent explicitly Pi01 for Con(SRP) about which we
recently posted.

It also features good clean implicitly Pi01 for Con(HUGE). There have
been problems finding an explicitly Pi01 for Con(HUGE) that is up to
the very high current standards.

Overall, this is our favorite implicitly Pi01 for Con(SRP), although
there are a large number of variants, some of which may be preferred
by various people.

(SQUARES). Every order invariant subset of Q[-n,n]^2k has a maximal
square whose sections at the x in {0,...,n}^r< have the same negative
part.

(ROOTS). Every order invariant subset of Q[-n,n]^2k has a maximal root
whose sections at the x in {0,...,n}^r< have the same negative part.

(GRAPHS). Every order invariant graph on Q[-n,n]^k has a maximal
clique whose sections at the x in {0,...,n}^r< have the same negative
part.

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My website is at https://u.osu.edu/friedman.8/ and my youtube site is at
https://www.youtube.com/channel/UCdRdeExwKiWndBl4YOxBTEQ
This is the 536th 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 #1-527 can be found at the FOM posting
http://www.cs.nyu.edu/pipermail/fom/2014-August/018092.html

528: More Perfect Pi01  8/16/14  5:19AM
529: Yet more Perfect Pi01 8/18/14  5:50AM
530: Friendlier Perfect Pi01
531: General Theory/Perfect Pi01  8/22/14  5:16PM
532: More General Theory/Perfect Pi01  8/23/14  7:32AM
533: Progress - General Theory/Perfect Pi01 8/25/14  1:17AM
534: Perfect Explicitly Pi01  8/27/14  10:40AM
535: Updated Perfect Explicitly Pi01  8/30/14  2:39PM

Harvey Friedman