STRONGLY MINIMAL PARTIAL ORDERINGS OF HEIGHT TWO
СИЛЬНО МИНИМАЛЬНЫЕ ЧАСТИЧНЫЕ ПОРЯДКИ ВЫСОТЫ ДВА
Kulpeshov B.Sh. Netaliyeva Ye.K.
2025Kazakh-British Technical University
Herald of the Kazakh British Technical UNiversity
2025#22Issue 1223 - 228 pp.
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.
connected component , maximal element , minimal element , partial ordering , strongly minimal structure
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Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Kazakh-British Technical University, Almaty, Kazakhstan
Institute of Mathematics and Mathematical Modeling
Kazakh-British Technical University
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