Sh:696

• Goldstern, M., & Shelah, S. (2002). Antichains in products of linear orders. Order, 19(3), 213–222. arXiv: math/9902054 DOI: 10.1023/A:1021289412771 MR: 1942184
• Abstract:
  We show that: For many cardinals \lambda, for all n\in \{2,3,4,\ldots\} 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,\ldots\}) 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^+.
• Version 2002-04-06_11 (9p) published version (10p)

@article{Sh:696,
 author = {Goldstern, Martin and Shelah, Saharon},
 title = {{Antichains in products of linear orders}},
 journal = {Order},
 fjournal = {Order. A Journal on the Theory of Ordered Sets and its Applications},
 volume = {19},
 number = {3},
 year = {2002},
 pages = {213--222},
 issn = {0167-8094},
 mrnumber = {1942184},
 mrclass = {06A05 (03E04 03E35)},
 doi = {10.1023/A:1021289412771},
 note = {\href{https://arxiv.org/abs/math/9902054}{arXiv: math/9902054}},
 arxiv_number = {math/9902054}
}