[FOM] Logic of irrational numbers

[joeshipman@aol.com]

Are you sure about this? It sounds like, if your conjecture is true, 
then Schanuel's Conjecture could not be a theorem of ZFC.

-- JS


-----Original Message-----
From: Harvey Friedman <friedman at math.ohio-state.edu>
To: Foundations of Mathematics <fom at cs.nyu.edu>
Sent: Wed, 4 Mar 2009 11:22 am
Subject: [FOM] Logic of irrational numbers



Here are two wild conjectures that people might find interesting.

For positive integers n and positive real numbers x, let x^[n] =
x^...^x, where there are n >= 1 x's.

WILD CONJECTURE 1. There exists n >= 1 such that "e^[n] is irrational"
can be proved using large cardinals, but not in ZFC.

WILD CONJECTURE 2. Various basic facts about {n: e^[n] is irrational}
can be proved using large cardinals, but not in ZFC.

I am not going to try to prove or refute these wild conjecture!

Harvey Friedman
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