[FOM] Large cardinals and finite combinatorics

[joeshipman@aol.com]

Yes, thanks for catching that typo. The first unknown case is whether 
there exists a Laver table with (1*1) not equal to (1*33) -- with 
rank-into-a-rank, one can show such an n exists, but Dougherty has 
shown that n is too big to be expressed without iterating the Ackermann 
function.  If such an n does exist, then this can be shown in a weak 
system, but possibly only with a proof of Ackermanic size.

-- JS


-----Original Message-----
From: Timothy Y. Chow <tchow at alum.mit.edu>

>
>It can be shown with large cardinals (using an embedding from a rank
>into a rank) that for any k there exists n such that, in the nth Laver
>table, (1*1) does not equal (1*(2^k)).

Do you mean 1*(2^k+1) here?

________________________________________________________________________
AOL now offers free email to everyone.  Find out more about what's free 
from AOL at AOL.com.