The Jónsson-Kiefer property

K. Adaricheva, R. McKenzie, E. R. Zenk, M. Maróti, J. B. Nation

Research output: Contribution to journalArticle

4 Citations (Scopus)

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| < 2א. 0, 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.

Original languageEnglish
Pages (from-to)111-131
Number of pages21
JournalStudia Logica
Volume83
Issue number1-3
DOIs
Publication statusPublished - Jun 1 2006

Keywords

  • Join semi-distributive lattice
  • Join-prime element
  • Meet semi-distributive lattice
  • Meet-prime element
  • Pseudo-complemented lattice

ASJC Scopus subject areas

  • Logic
  • History and Philosophy of Science

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  • Cite this

    Adaricheva, K., McKenzie, R., Zenk, E. R., Maróti, M., & Nation, J. B. (2006). The Jónsson-Kiefer property. Studia Logica, 83(1-3), 111-131. https://doi.org/10.1007/s11225-006-8300-x