[FOM] Finite functions and necessary use of large cardinals

Joe Shipman joeshipman at aol.com
Tue Nov 12 12:05:18 EST 2019

This is quite striking. Harvey can probably shed light on whether the subclass of graph theorems that you can derive from P=NP as well as from subtle cardinals is sufficiently broad that his “reversals” can be adapted to them. If so, then you will have shown that P=NP is independent and P!=NP is consistent.  

If not, i.e. if the subclass of graph theorems is narrow enough to be provable in ZFC,  then this may shed light on the subset sum problem, although it seems unlikely that the relevant easy instances of subset sum will threaten to entail P=NP (because we already know that subset sum is not very strongly NP-complete, being PTIME approximable and pseudo-Ptime solvable).

— JS

Sent from my iPhone

> On Nov 12, 2019, at 11:36 AM, S. Gill Williamson <gill.williamson at gmail.com> wrote:
> Below is a link to my latest thoughts on connections between Harvey Friedman's 1998 paper (Annals of Mathematics) and the P vs NP problem:
> -- Gill Williamson
> https://arxiv.org/abs/1907.11707v2
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