A note on Dilworth's theorem in the infinite case

Uri Abraham

doi:10.1007/BF00337691

A note on Dilworth's theorem in the infinite case

Uri Abraham

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

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 language	English
Pages (from-to)	107-125
Number of pages	19
Journal	Order
Volume	4
Issue number	2
DOIs	https://doi.org/10.1007/BF00337691
State	Published - 1 Jun 1987

Keywords

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

ASJC Scopus subject areas

Algebra and Number Theory
Geometry and Topology
Computational Theory and Mathematics

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10.1007/BF00337691

Cite this

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AB - 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.

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KW - Poset

KW - antichain

KW - chain

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A note on Dilworth's theorem in the infinite case

Abstract

Keywords

ASJC Scopus subject areas

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