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 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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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