For u ∈ V let Max (u) denote the family of all finite maximal antichains in E u N https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203741306/c55385f7-2580-4d5d-9edc-159ef372c866/content/inequ5_1.tif"/> , i.e. Γ ∈ Max (u) if and only if Γ is a finite subset of E u ( * ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203741306/c55385f7-2580-4d5d-9edc-159ef372c866/content/inequ5_2.tif"/> and for each σ ∈ E u N https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203741306/c55385f7-2580-4d5d-9edc-159ef372c866/content/inequ5_3.tif"/> there is a unique γ ∈Γ such that σ ∈ [γ]. For Γ ∈ Max(u) write