Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

The Jónsson-Kiefer Property

Kira Adaricheva, Miklos Maróti, Ralph McKenzie, J. B. Nation and Eric R. Zenk
Studia Logica: An International Journal for Symbolic Logic
Vol. 83, No. 1/3, Special Issue in Memory of Willem Johannes Blok (Jun. - Aug., 2006), pp. 111-131
Published by: Springer
Stable URL: http://www.jstor.org/stable/20016801
Page Count: 21
  • Download ($43.95)
  • Cite this Item
The Jónsson-Kiefer Property
Preview not available

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 $|L|<2^{\aleph _{0}}$, 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 $|L|=|L_{c}|=2^{\aleph _{0}}$ where $L_{c}$ is the set of compact elements of L.

Page Thumbnails

  • Thumbnail: Page 
[111]
    [111]
  • Thumbnail: Page 
112
    112
  • Thumbnail: Page 
113
    113
  • Thumbnail: Page 
114
    114
  • Thumbnail: Page 
115
    115
  • Thumbnail: Page 
116
    116
  • Thumbnail: Page 
117
    117
  • Thumbnail: Page 
118
    118
  • Thumbnail: Page 
119
    119
  • Thumbnail: Page 
120
    120
  • Thumbnail: Page 
121
    121
  • Thumbnail: Page 
122
    122
  • Thumbnail: Page 
123
    123
  • Thumbnail: Page 
124
    124
  • Thumbnail: Page 
125
    125
  • Thumbnail: Page 
126
    126
  • Thumbnail: Page 
127
    127
  • Thumbnail: Page 
128
    128
  • Thumbnail: Page 
129
    129
  • Thumbnail: Page 
130
    130
  • Thumbnail: Page 
131
    131