Аңдатпа
Abstract In the present paper, we study strongly minimal partial orderings in the signature containing only the symbol of binary relation for a 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. 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 such partial orderings.