Cardinalities of infinite antichains in products of chains.

In response to a question of Ploščica and Haviar, a chain L is constructed such that $L^3$ has an antichain of infinite cardinality $\kappa$ while $L^2$ does not. The construction applies to any singular $\kappa$ . (Independently, such chains have been constructed for certain regular $\kappa$ by Goldstern and Shelah.) [ABSTRACT FROM AUTHOR]