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 |
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Pages (from-to) | 111-131 |
Number of pages | 21 |
Journal | Studia Logica |
Volume | 83 |
Issue number | 1-3 |
DOIs | |
Publication status | Published - Jun 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