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 2006
Externally publishedYes

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Distributive Lattice
Semilattice
Join
Distributive

Keywords

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

ASJC Scopus subject areas

  • Logic

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

The Jónsson-Kiefer property. / Adaricheva, K.; McKenzie, R.; Zenk, E. R.; Maróti, M.; Nation, J. B.

In: Studia Logica, Vol. 83, No. 1-3, 06.2006, p. 111-131.

Research output: Contribution to journalArticle

Adaricheva, K, McKenzie, R, Zenk, ER, Maróti, M & Nation, JB 2006, 'The Jónsson-Kiefer property', Studia Logica, vol. 83, no. 1-3, pp. 111-131. https://doi.org/10.1007/s11225-006-8300-x
Adaricheva K, McKenzie R, Zenk ER, Maróti M, Nation JB. The Jónsson-Kiefer property. Studia Logica. 2006 Jun;83(1-3):111-131. https://doi.org/10.1007/s11225-006-8300-x
Adaricheva, K. ; McKenzie, R. ; Zenk, E. R. ; Maróti, M. ; Nation, J. B. / The Jónsson-Kiefer property. In: Studia Logica. 2006 ; Vol. 83, No. 1-3. pp. 111-131.
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