[FOM] A question about references

Kreinovich, Vladik vladik at utep.edu
Sat Jan 7 12:02:08 EST 2017

For arithmetic equivalent of the Riemann hypothesis, see http://mathoverflow.net/questions/32892/does-anyone-know-a-polynomial-whose-lack-of-roots-cant-be-proved

It mentions a paper with Boris Moroz which is no longer available at the place where it was posted, I am copying Dr. Moroz so that he will be able to provide an updated location of this paper

-----Original Message-----
From: fom-bounces at cs.nyu.edu [mailto:fom-bounces at cs.nyu.edu] On Behalf Of Arnon Avron
Sent: Saturday, January 07, 2017 12:02 AM
To: Foundations of Mathematics <fom at cs.nyu.edu>
Cc: Arnon Avron <aa at tau.ac.il>
Subject: [FOM] A question about references

In his recent posting about incompleteness Friedman quoted the following from Scott Aaronson:

"(2)  Independence of statements in transfinite set theory, such as CH and AC. Unlike "ordinaryâ" mathematical statements --- P ̸= NP, the Riemann hypothesis, etc. the set-theoretic ones can't be rephrased in the language of elementary arithmetic; only questions about their provability from various axiom systems are arithmetical."

My question: what are the best sources in which the most updated (and perhaps even not the most updated) rephrasing of P ̸= NP, the Riemann hypothesis, etc in the language of elementary arithmetic can be found (and the equivalences are proved)?


Arnon Avron
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