[FOM] 461: Reflections on Vienna Meeting

[Harvey Friedman]

On Jun 14, 2011, at 12:19 PM, Harvey Friedman wrote:

> Modulo some very interesting issues in f.o.m., particularly reverse  
> math and strict reverse math, a consequence of this quote is
>
> "none of us know whether an infinite sequence of rationals from  
> [0,1] has an infinite 1/n style Cauchy subsequence"
>
> a claim that I am sure Angus would not subscribe to.
>
> Angus, can you explain your position?

Let me add that modulo some interesting strict reverse mathematics,  
the statement

"every infinite sequence of rationals from [0,1] has an infinite 1/n  
style Cauchy subsequence"

outright implies (and is used by a large number of mathematicians  
Angus has no reservations about)

"PA restricted to 100 quantifier inductions is consistent".

Here 100 can of course be replaced by any positive integer. The length  
of the derivation corresponds to the number of quantifiers.

Harvey Friedman