antichain
antichain noun: a subset, A, of a partially ordered set, (P, ≤), such that no two elements of A are comparable with respect to ≤.
Noun
antichain (plural antichains)
- 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
- 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.2013, Vijay K. Garg, Maximal Antichain Lattice Algorithms for Distributed Computations, Proceedings, Davide Frey, Michel Raynal, Saswati Sarkar, Rudrapatna K. Shyamasundar, Prasun Sinha (editors)...
Forms of antichain
| plural | antichains |
|---|
Origin of antichain
From anti- + chain.
Words formed from antichain
- maximal antichain
Questions about antichain
- What does antichain mean?
- Antichain means a subset, A, of a partially ordered set, (P, ≤), such that no two elements of A are comparable with respect to ≤.
- What part of speech is antichain?
- Antichain is a noun.
- What is the plural of antichain?
- The plural of antichain is antichains.
Words near antichain in the dictionary
Source and license
Adapted from Wiktionary: antichain (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.
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