[FOM] 821: Beyond Perfectly Natural/18

[Harvey Friedman]

I found some ridiculous typos in

https://u.osu.edu/friedman.8/foundational-adventures/downloadable-lecture-notes-2/
   #69

and alerted everybody on that page, rather than edit the slides. I
have kept the slides exactly as they were during the talk.

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There is still considerable room for putting the FINITE FORM of MES in
more striking form.

I have made some significant improvements in Finite MES and have put
up a new version of this

https://u.osu.edu/friedman.8/foundational-adventures/downloadable-manuscripts/
   #106, June 17, 2018

Below, I copy the new form here and the two variants, and you can look
there to see the rather straightforward supporting definitions.

FINITE MAXIMAL EMULATION STABILITY. FMES. Let n > (8k)!. Every subset
of [kn]^k has a stable emulator S, where in S^k x n[k]^k x [kn]^k,
every element is order equivalent to a resolved element.

FINITE MAXIMAL EMULATION STABILITY(full). FMES(full). Let n > (8kr)!.
Every subset of [kn]^k has a fully stable r-emulator S, where in S^k x
n[k]^k x [kn]^k, every element is order equivalent to a resolved
element.

GENERAL FINITE MAXIMAL EMULATION STABILITY. GFMES. Let n > (8kr)!.
Every subset of [kn]^k has a fully stable r-emulator S, where in S^k x
n[k]^k x [kn]^k, every element is order equivalent to a step resolved
element.

THEOREM 6.3. FMES, FMES(full), GFMES are equivalent to Con(SRP) over EFA.

************************************************************************
My website is at https://u.osu.edu/friedman.8/ and my youtube site is at
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This is the 821st 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
814: Beyond Perfectly Natural/13  6/3/18  2:05PM
815: Beyond Perfectly Natural/14  6/5/18  9:41PM
816: Beyond Perfectly Natural/15  6/8/18  1:20AM
817: Beyond Perfectly Natural/16  Jun 13 01:08:40
818: Beyond Perfectly Natural/17  6/13/18  4:16PM
819: Sugared ZFC Formalization/1  6/13/18  6:42PM
820: Sugared ZFC Formalization/2  6/14/18  6:45PM

Harvey Friedman