Finite distributive lattices and the splitting property
β Scribed by Dwight Duffus; Bill Sands
- Publisher
- Springer
- Year
- 2003
- Tongue
- English
- Weight
- 317 KB
- Volume
- 49
- Category
- Article
- ISSN
- 0002-5240
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
For a finite ordered set G let ~(G) denote the family of all distributive lattices L such that G both generates L and is the set of doubly irreducible elements of L. We provide a characterization for membership in ~(G), and by means of this characterization define a natural order relation on ~(G). W
The following conjecture of U Faigle and B Sands is proved: For every number R > 0 there exists a number n(R) such that if 2 is a finite distributive lattice whose width w(Z) (size of the largest antichain) is at least n(R), then IZ/a Rw(Z). In words this says that as one considers ~ increasingly la
If the Liikasiewicz many-valued systems are treated as logics in the senst of the following section, to whirh a sequent belongs wlien every assignment of trut,h-ralues giving a deliignakcd value to every formnla on the left of the "I-" gives a designated value to the formula on the right, then these