Article · Lobachevskii Journal of Mathematics · April 1, 2026
Strongly Minimal Partial Orderings Having an Infinite Non-trivial Width
B. Sh. Kulpeshov, Ye. K. Netaliyeva
Abstract
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.
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