Antichain

Quick meaning: Antichain is a noun meaning (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 ≤.

Meaning

(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 ≤.

Example Sentences

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.

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.

Word Forms

• antichains

Related Words

Related dictionary entries include chain, multichain, well-order, order, poset, quasiorder.

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