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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