منابع مشابه
Large semilattices of breadth three
A 1984 problem of S. Z. Ditor asks whether there exists a lattice of cardinality א2, with zero, in which every principal ideal is finite and every element has at most three lower covers. We prove that the existence of such a lattice follows from either one of two axioms that are known to be independent of ZFC, namely (1) Martin’s Axiom restricted to collections of א1 dense subsets in posets of ...
متن کاملSemilattices of Breadth Three
A 1984 problem of S. Z. Ditor asks whether there exists a lattice of cardinality א2, with zero, in which every principal ideal is finite and every element has at most three lower covers. We prove that the existence of such a lattice follows from either one of two axioms that are known to be independent of ZFC, namely (1) Martin’s Axiom restricted to collections of א1 dense subsets in posets of ...
متن کاملOf Breadth Three
A 1984 problem of S. Z. Ditor asks whether there exists a lattice of cardinality א2, with zero, in which every principal ideal is finite and every element has at most three lower covers. We prove that the existence of such a lattice follows from either one of two axioms that are known to be independent of ZFC, namely (1) Martin’s Axiom restricted to collections of א1 dense subsets in posets of ...
متن کاملLarge-Scale Parallel Breadth-First Search
Recently, best-first search algorithms have been introduced that store their nodes on disk, to avoid their inherent memory limitation. We introduce several improvements to the best of these, including parallel processing, to reduce their storage and time requirements. We also present a linear-time algorithm for bijectively mapping permutations to integers in lexicographic order. We use breadth-...
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The main result of this paper is that the class of congruence lattices of semilattices satisfies no nontrivial lattice identities. It is also shown that the class of subalgebra lattices of semilattices satisfies no nontrivial lattice identities. As a consequence it is shown that if 5^* is a semigroup variety all of whose congruence lattices satisfy some fixed nontrivial lattice identity, then a...
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 2010
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm208-1-1