# Sh:696

• Goldstern, M., & Shelah, S. (2002). Antichains in products of linear orders. Order, 19(3), 213–222.
• 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^+.
• Current version: 2002-04-06_11 (9p) published version (10p)
Bib entry
@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}
}