Studia Logica

, Volume 83, Issue 1, pp 111–131

The Jónsson-Kiefer Property

  • K. Adaricheva
  • R. Mckenzie
  • E. R. Zenk
  • M. Mar´ti
  • J. B. Nation
Article

DOI: 10.1007/s11225-006-8300-x

Cite this article as:
Adaricheva, K., Mckenzie, R., Zenk, E.R. et al. Stud Logica (2006) 83: 111. doi:10.1007/s11225-006-8300-x

Abstract

The least element 0 of a finite meet semi-distributive lattice is a meet of meet-prime elements. We investigate conditions under which the least element of an algebraic, meet semi-distributive lattice is a (complete) meet of meet-prime elements. For example, this is true if the lattice has only countably many compact elements, or if |L| < 2ℵ0, or if L is in the variety generated by a finite meet semi-distributive lattice. We give an example of an algebraic, meet semi-distributive lattice that has no meet-prime element or join-prime element. This lattice L has |L| = |LC| = 2ℵ0 where Lc is the set of compact elements of L.

Keywords

Meet semi-distributive lattice pseudo-complemented lattice meet-prime element join semi-distributive lattice join-prime element 

Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  • K. Adaricheva
    • 1
  • R. Mckenzie
    • 2
  • E. R. Zenk
    • 2
  • M. Mar´ti
    • 3
  • J. B. Nation
    • 4
  1. 1.Department of MathematicsHarold Washington CollegeChicagoUSA
  2. 2.Department of Mathematics 1326 Stevenson CenterVanderbilt UniversityNashvilleUSA
  3. 3.Bolyai InstituteUniversity of SzegedSzegedHungary
  4. 4.Department of MathematicsUniversity of Hawaii at ManoaHonoluluUSA

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