A note on Dilworth's theorem in the infinite case

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Abstract

If ℘ is a poset and every antichain is finite, and if the length of the well-founded poset of antichains is less than ω21, then ℘ is the union of countably many chains. We also compute the length of the poset of antichains in the product of two ordinals, αxβ.

Original languageEnglish
Pages (from-to)107-125
Number of pages19
JournalOrder
Volume4
Issue number2
DOIs
StatePublished - 1 Jun 1987

Keywords

  • AMS subject classifications (1980): 03E05 Combinatorial set theory, 03E10 Ordinal and cardinal numbers, 06A10 Partial order
  • Poset
  • antichain
  • chain

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