منابع مشابه
Chains and antichains in partial orderings
We study the complexity of infinite chains and antichains in computable partial orderings. We show that there is a computable partial ordering which has an infinite chain but none that is Σ1 or Π 1 1, and also obtain the analogous result for antichains. On the other hand, we show that every computable partial ordering which has an infinite chain must have an infinite chain that is the differenc...
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We introduce a list of classes of relational structures obtained from chains, antichains, and indicators, and we show which of them are Fraïssé classes. In addition to this, we classify these classes according to the Ramsey property.
متن کاملMaximal Chains and Antichains in Boolean Lattices
The following equivalent results in the Boolean lattice 2 are proven. (a) Every fibre of 2 contains a maximal chain. (b) Every cutset of 2 contains a maximal antichain. (c) Every red-blue colouring of the vertices of 2 produces either a red maximal chain or a blue maximal antichain. (d) Given any n antichains in 2 there is a disjoint maximal antichain. Statement (a) is then improved to: (a') Ev...
متن کاملDescending Chains and Antichains of the Unary, Linear, and Monotone Subfunction Relations
The C-subfunction relations on the set of operations on a finite base set A defined by function classes C are examined. For certain clones C on A, it is determined whether the partial orders induced by the respective C-subfunction relations have infinite descending chains or infinite antichains. More specifically, we investigate the subfunction relations defined by the clone of all functions on...
متن کاملGeneral relations between partially ordered multisets and their chains and antichains
In this paper we begin with the basics of multisets and their operations introduced in [5, 22] and define a multiset relation, an equivalence multiset relation and explore some of their basic properties. We also define a partially ordered multiset as a multiset relation being reflexive, antisymmetric and transitive, chains and antichains of a partially ordered multiset, and extend Dilworth’s Th...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 1986
ISSN: 0195-6698
DOI: 10.1016/s0195-6698(86)80009-9