The Jónsson-Kiefer Property
نویسندگان
چکیده
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| < 2א0 , 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.
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ورودعنوان ژورنال:
- Studia Logica
دوره 83 شماره
صفحات -
تاریخ انتشار 2006