Diamond and antichains

It is obvious that implies the existence of an antichain of stationary sets of cardinality which is the largest possible cardinality. We show that the obvious antichain is not maximal and find a less obvious extension of it by ₂ more stationary sets.Mathematics Subject Classification (2000): 03EThe research of the authors is partially supported by the NSF.The second author was partially supported by IHES during his June 5–25, 2002, visit. He thanks Stevo Todorcevic and Boban Velickovic for conversations during the visit on the main question answered in this report.