[FOM] 815: Beyond Perfectly Natural/14

Harvey Friedman hmflogic at gmail.com
Tue Jun 5 21:41:29 EDT 2018

There is a new manuscript on site:


  106. Everybody’s Mathematics – Maximal Emulation Stability, 12
pages, June 5, 2018. Focuses on MES, the lead statement in Emulation
Theory. Presents finite solitaire games as explicitly Pi01 forms, and
their prospective use for the confirmation of the consistency of
mathematics. Also see Downloadable Lecture Notes #69 for the slides
from the recent talk rolling out Maximal Emulation Stability.


Abstract. MES is Maximal Emulation Stability, the lead statement in
the new Emulation Theory. MES asserts that every finite subset of
Q[0,k]^k has a stable maximal emulator. MES is sufficiently natural,
transparent, concrete, elementary, interesting, memorable, teachable,
rich in varied intricate examples, and rich in weaker and stronger
forms, that it merits being classified in the category of Everybody's
Mathematics. MES is readily seen, via Goedel's Completeness Theorem, to
be implicitly Pi01. MES is independent of the usual ZFC axioms for
mathematics, and is actually equivalent to Con(SRP) over WKL_0. We
also discuss GMES = General Maximal Emulation Stability, a natural
generalization, with the same metamathematical properties. We conclude
with explicitly Pi01 forms in the shape of playable solitaire games.
We argue that winning these games can be construed as confirmation of
the consistency of mathematics.

1. Introduction.
2. Maximal Emulation Stability (MES).
3. Emulation Variants.
4. Stability Variants.
5. General MES.
6. Finite Solitaire Games.
7. Confirming Consistency of Mathematics.
8. Formal Systems Used.
9. References.

Sections 6,7 in the above paper contains a new approach to Explicitly
Pi01 Forms via deliciously simple Solitaire Games that can be actually
played, and used to Confirm the Consistency of Mathematics (arguably).
This could lead to a really serious Application of SAT to Consistency
of Mathematics.

My website is at https://u.osu.edu/friedman.8/ and my youtube site is at
This is the 815th 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

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

Harvey Friedman

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