[FOM] 814: Beyond Perfectly Natural/13
Harvey Friedman
hmflogic at gmail.com
Sun Jun 3 14:05:58 EDT 2018
In https://cs.nyu.edu/pipermail/fom/2018-May/021019.html I discussed
my recent talk at
https://u.osu.edu/friedman.8/foundational-adventures/downloadable-manuscripts/
#69.
At the end of that posting, I discussed a finite form of MES that
appears at the end of that talk, page 32. On page 10 of the talk I
warn everybody that I don't want to talk about 12 hour old "results".
It turns out that that was good advice. I have struggled quite a bit
to find better and better finite forms in Emulation Theory, with
plenty of false starts. So I retract page 32 (as indicated on my
website), and also the corresponding last part of the previous FOM
posting #813.
Here is a new version, full of confidence, which I LIKE BETTER ANYWAY.
*FINITE MES*
in {0,...,kn}^k
Let E containedin {0,...,kn}^k. S is an emulator of E if and only if S
containedin {0,...,kn}^k and every element of S^2 is order equivalent
to an element of E^2. S is a maximal emulator of E containedin
{0,...,kn}^k if and only if S is an emulator of E containedin
{0,...,kn}^k which is not a proper subset of any emulator of E
contaiendin {0,...,kn}^k. We can say this more vividly this way: S is
ruined by any new element from {0,...,kn}^k.
E is stable if and only if for all 0 <= i < n, (i,n,2n,...,(k-1)n) in
E if and only if (i,2n,3n,...,kn) in E.
The mix of E is the set of all elements of {0,...,kn}^k whose
coordinates are all coordinates of elements of E.
FINITE MAXIMAL EMULATION STABILITY. FMES. Assume n > (8kr)!. Every
subset of {0,...,kn}^k has a length r tower of stable emulations,
where each term is ruined by any new element from {0,n,2n,...,kn}^k
and by any new element from the mixes of the previous terms.
FMES is obviously explicitly Pi01.
THEOREM 1. FMES, FMES for r = 3 are both equivalent to Con(SRP) over
EFA. There is a hierarchy through Con(SRP) obtained by fixing k.
************************************************************************
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 814th 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 #1-799 can be found at
http://u.osu.edu/friedman.8/foundational-adventures/fom-email-list/
800: Beyond Perfectly Natural/6 4/3/18 8:37PM
801: Big Foundational Issues/1 4/4/18 12:15AM
802: Systematic f.o.m./1 4/4/18 1:06AM
803: Perfectly Natural/7 4/11/18 1:02AM
804: Beyond Perfectly Natural/8 4/12/18 11:23PM
805: Beyond Perfectly Natural/9 4/20/18 10:47PM
806: Beyond Perfectly Natural/10 4/22/18 9:06PM
807: Beyond Perfectly Natural/11 4/29/18 9:19PM
808: Big Foundational Issues/2 5/1/18 12:24AM
809: Goedel's Second Reworked/1 5/20/18 3:47PM
810: Goedel's Second Reworked/2 5/23/18 10:59AM
811: Big Foundational Issues/3 5/23/18 10:06PM
812: Goedel's Second Reworked/3 5/24/18 9:57AM
813: Beyond Perfectly Natural/12 05/29/18 6:22AM
Harvey Friedman
More information about the FOM
mailing list