[FOM] Large cardinals and finite combinatorics
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.
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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