[FOM] Logic of irrational numbers

[Harvey Friedman]

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