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 language | English |
|---|---|
| Pages (from-to) | 111-131 |
| Number of pages | 21 |
| Journal | Studia Logica |
| Volume | 83 |
| Issue number | 1-3 |
| DOIs | |
| Publication status | Published - Jun 2006 |
| Externally published | Yes |
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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
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 journal › Article
}
TY - JOUR
T1 - The Jónsson-Kiefer property
AU - Adaricheva, K.
AU - McKenzie, R.
AU - Zenk, E. R.
AU - Maróti, M.
AU - Nation, J. B.
PY - 2006/6
Y1 - 2006/6
N2 - 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.
AB - 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.
KW - Join semi-distributive lattice
KW - Join-prime element
KW - Meet semi-distributive lattice
KW - Meet-prime element
KW - Pseudo-complemented lattice
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UR - http://www.scopus.com/inward/citedby.url?scp=33746116498&partnerID=8YFLogxK
U2 - 10.1007/s11225-006-8300-x
DO - 10.1007/s11225-006-8300-x
M3 - Article
VL - 83
SP - 111
EP - 131
JO - Studia Logica
JF - Studia Logica
SN - 0039-3215
IS - 1-3
ER -