[FOM] 529: Yet More Perfect Pi01

[Harvey Friedman]

I have upgraded the extended abstract #82
https://u.osu.edu/friedman.8/foundational-adventures/downloadable-manuscripts/
with independent implicity Pi01 statements involving equal sections below
1.

ORDER INVARIANT RELATIONS AND INCOMPLETENESS
by
Harvey M. Friedman*
Distinguished University Professor of Mathematics, Philosophy, and Computer
Science Emeritus
Ohio State University
August 18, 2014
EXTENDED ABSTRACT

*This research was partially supported by the John Templeton Foundation
grant ID #36297. The opinions expressed here are those of the author and do
not necessarily reflect the views of the John Templeton Foundation.

Abstract. Every order invariant subset of Q[0,n]^2k has a maximal square
whose sections at strictly increasing r tuples of positive integers agree
below 1. Every order invariant graph on Q[0,n]^k has a maximal clique whose
sections at strictly increasing r tuples of positive integers agree below
1. Every order invariant graph on Q^k has a step maximal clique whose
sections at blocks of r positive integers agree below 1. We prove these and
closely related statements, including a finite form, in extensions of the
usual ZFC axioms for mathematics with standard large cardinal hypotheses,
and show that ZFC does not suffice (assuming ZFC is consistent).

The book will probably have the tentative title ORDER INVARIANCE AND
INCOMPLETENESS.

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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 528th 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

Harvey Friedman
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