# 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^+. - 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}, doi = {10.1023/A:1021289412771}, mrclass = {06A05 (03E04 03E35)}, mrnumber = {1942184}, mrreviewer = {Aleksander Rutkowski}, doi = {10.1023/A:1021289412771}, note = {\href{https://arxiv.org/abs/math/9902054}{arXiv: math/9902054}}, arxiv_number = {math/9902054} }