[FOM] Large cardinals and finite combinatorics

joeshipman@aol.com joeshipman at aol.com
Mon Jun 18 23:18:14 EDT 2007

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?

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