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.
Source: wiktionary
Antichain
Synonyms for "antichain"
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4 entriesTranslations
3 translations across 3 languages.
Finnish
1 entries- antiketju noun (subset of a partially ordered set)
Italian
1 entries- anticatena noun (subset of a partially ordered set)
Spanish
1 entries- anticadena noun (subset of a partially ordered set)
Sample sentences
2 total sentences available.
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.
Source: wiktionary
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Data sourced from Wiktionary, WordNet, CMU, and other open linguistic databases. Updated March 2026.