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algebra universalis

, Volume 53, Issue 2–3, pp 287–299 | Cite as

Which posets have a scattered MacNeille completion?

  • Maurice PouzetEmail author
  • Hamza Si Kaddour
  • Nejib Zaguia
Original Paper

Abstract.

A poset is order-scattered if it does not embed the chain η of the rational numbers. We prove that there are eleven posets such that N(P), the MacNeille completion of P, is order-scattered if and only if P embeds none of these posets. Moreover these posets are pairwise non-embeddable in each other. This result completes a previous characterisation due to Duffus, Pouzet, Rival [4]. The proof is based on the “bracket relation”: \(\eta \to [\eta ]^{2}_{3} ,\) a famous result of F. Galvin.

Mathematics Subject Classification (2000).

06A07 06B23 03E02 

Key words and phrases.

MacNeille completion scattered posets partition theorems 

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Copyright information

© Birkhäuser Verlag, Basel 2005

Authors and Affiliations

  • Maurice Pouzet
    • 1
    Email author
  • Hamza Si Kaddour
    • 1
  • Nejib Zaguia
    • 2
  1. 1.LaPCS, MathématiquesUniversité Claude-BernardVilleurbanneFrance
  2. 2.SITEUniversité d’OttawaOttawaCanada

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