Search results for "Congruence lattice problem"
showing 3 items of 3 documents
From Lattice Valued Theories to Lattice Valued Analysis
2015
We claim and justify that the future of a fuzzy logic is in the interconnection of various well-developed theories. We are focused on a lattice valued analysis that unifies the treatments of atomic elements, sets of atomic elements, functions between sets of atomic elements and their properties. We clarify the relationship between a fuzzy function and its ordinary core. We discuss the property of continuity of a fuzzy function in a lattice valued topology.
The completely distributive lattice of machine invariant sets of infnite words
2007
Posets That Locally Resemble Distributive Lattices
2000
Abstract Let P be a graded poset with 0 and 1 and rank at least 3. Assume that every rank 3 interval is a distributive lattice and that, for every interval of rank at least 4, the interval minus its endpoints is connected. It is shown that P is a distributive lattice, thus resolving an issue raised by Stanley. Similar theorems are proven for semimodular, modular, and complemented modular lattices. As a corollary, a theorem of Stanley for Boolean lattices is obtained, as well as a theorem of Grabiner (conjectured by Stanley) for products of chains. Applications to incidence geometry and connections with the theory of buildings are discussed.