Antichain

noun

noun ·Rare ·Advanced level

Definitions

Noun
  1. 1
    A subset, A, of a partially ordered set, (P, ≤), such that no two elements of A are comparable with respect to ≤. error-lua-exec

    "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."

Example

More examples

"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."

Etymology

From anti- + chain.

Related phrases

maximal antichainpartially ordered set

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Data sourced from Wiktionary, WordNet, CMU, and other open linguistic databases. Updated March 2026.