Disjoint sequences and completeness properties
نویسندگان
چکیده
منابع مشابه
Completeness Properties of Perturbed Sequences
If S is an arbitrary sequence of positive integers, let P(S) be the set of all integers which are representable as a sum of distinct terms of S . Call S complete if P(S) contains all large integers, and subcomplete if P(S) contains an infinite arithmetic progression . It is shown that any sequence can be perturbed in a rather moderate way into a sequence which is not subcomplete . On the other ...
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We study the question of whether the class DisjNP of disjoint pairs (A,B) of NPsets contains a complete pair. The question relates to the question of whether optimal proof systems exist, and we relate it to the previously studied question of whether there exists a disjoint pair of NP-sets that is NP-hard. We show under reasonable hypotheses that nonsymmetric disjoint NP-pairs exist, which provi...
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We describe two opposing combinatorial properties related to adding clubs to ω2: the existence of a thin stationary subset of Pω1 (ω2) and the existence of a disjoint club sequence on ω2. A special Aronszajn tree on ω2 implies there exists a thin stationary set. If there exists a disjoint club sequence, then there is no thin stationary set, and moreover there is a fat stationary subset of ω2 wh...
متن کاملNearly Disjoint Sequences in Convergence -groups
For an abelian lattice ordered group G let convG be the system of all compatible convergences on G; this system is a meet semilattice but in general it fails to be a lattice. Let αnd be the convergence on G which is generated by the set of all nearly disjoint sequences in G, and let α be any element of convG. In the present paper we prove that the join αnd ∨ α does exist in convG.
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A Skolem sequence is a sequence a1, a2, . . . , a2n (where ai ∈ A = {1, . . . , n}), each ai occurs exactly twice in the sequence and the two occurrences are exactly ai positions apart. A set A that can be used to construct Skolem sequences is called a Skolem set. The existence question of deciding which sets of the form A = {1, . . . , n} are Skolem sets was solved by Thoralf Skolem [6] in 195...
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ژورنال
عنوان ژورنال: Indagationes Mathematicae (Proceedings)
سال: 1985
ISSN: 1385-7258
DOI: 10.1016/s1385-7258(85)80016-0