### Antichains in products of linear orders

by Goldstern and Shelah. [GoSh:696]

Order, 2002

We show that: For many cardinals lambda, for all
n in {2,3,4, ...} There is a linear order L such that
L^n has no (incomparability-)antichain of cardinality
lambda, while L^{n+1} has an antichain of cardinality
lambda . For any nondecreasing sequence (lambda_n: n in
{2,3,4, ...}) of infinite cardinals it is consistent that
there is a linear order L such that L^n has an antichain
of cardinality lambda_n, but not one of cardinality
lambda_n^+ .

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