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Antichains in products of linear orders

Martin Goldstern·Saharon Shelah
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Abstract

1. For many regular cardinals lambda (in particular, for all successors of singular strong limit cardinals, and for all successors of singular omega-limits), 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 . 2. For any nondecreasing sequence (lambda2,lambda3, ...) 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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Martin Goldstern, Saharon Shelah. 1999-02-08. Antichains in products of linear orders. https://arxiv.org/abs/math/9902054

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