STRONGLY MINIMAL PARTIAL ORDERINGS OF HEIGHT TWO
Beibut Shaiykovich Kulpeshov, Ye. K. Netaliyeva · Herald of Kazakh-British technical university · 2025
In the present paper, we study strongly minimal partial orderings in the signature containing only the symbol of binary relation of partial order. We use for partial orderings such characteristics as the height of a structure that is the supremum of lengths of ordered chains, and the width of a structure that is the supremum of lengths of antichains, where an antichain is a set of pairwise incomparable elements. We also differ trivial width and non-trivial width. Recently, B.Sh. Kulpeshov, In.I. Pavlyuk and S.V. Sudoplatov described strongly minimal partial orderings having a finite non-trivial width. Here we study strongly minimal partial orderings having an infinite non-trivial width. The main result of the paper is a criterion for strong minimality of an infinite partial ordering of height two having an infinite non-trivial width.