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Pronunciation varies by accent · noun
(set theory, order theory, graph theory) A subset, A, of a partially ordered set, (P, ≤), such that no two elements of A are comparable with respect to ≤..
2013, Vijay K. Garg, Maximal Antichain Lattice Algorithms for Distributed Computations, Proceedings, Davide Frey, Michel Raynal, Saswati Sarkar, Rudrapatna K. Shyamasundar, Prasun Sinha (editors), Distributed Computing and Networking: 14th International Conference, ICDCN, Springer, LNCS 7730, page 245, We first define three different but isomorphic lattices: the lattice of maximal antichain ideals, the lattice of maximal antichains and the lattice of strict ideals.
First of all, Zorn's Lemma implies that every uncountable antichain in T is contained in a maximal uncountable antichain. So it suffices to make sure that T has no maximal uncountable antichains.
Use antichain when its meaning, tone and grammar fit the full sentence. A synonym is not always a direct replacement.
Antichain means (set theory, order theory, graph theory) A subset, A, of a partially ordered set, (P, ≤), such that no two elements of A are comparable with respect to ≤..
The closest synonym depends on the sentence and intended sense.
The opposite depends on the specific sense.
2013, Vijay K. Garg, Maximal Antichain Lattice Algorithms for Distributed Computations, Proceedings, Davide Frey, Michel Raynal, Saswati Sarkar, Rudrapatna K. Shyamasundar, Prasun Sinha (editors), Distributed Computing and Networking: 14th International Conference, ICDCN, Springer, LNCS 7730, page 245, We first define three different but isomorphic lattices: the lattice of maximal antichain ideals, the lattice of maximal antichains and the lattice of strict ideals.
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