antichain
nounEtymology From anti- + chain.
1
Graph theory, Mathematics, Order theory, Sciences, Set theory A subset, A, of a partially ordered set, (P, ≤), such that no two elements of A are comparable with respect to ≤.
- 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.1997, Winfried Just, Martin Weese, Discovering Modern Set Theory II: Set-Theoretic Tools for Every Mathematician, American Mathematical Society, page 140:
- 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.
- Derived terms
- maximal antichain