منابع مشابه
Reconstructing Subsets of Reals
We consider the problem of reconstructing a set of real numbers up to translation from the multiset of its subsets of fixed size, given up to translation. This is impossible in general: for instance almost all subsets of Z contain infinitely many translates of every finite subset of Z. We therefore restrict our attention to subsets of R which are locally finite; those which contain only finitel...
متن کاملReconstructing Subsets of Zn
In this paper we consider the problem of reconstructing a subset A ⊂ Z n , up to translation, from the collection of its subsets of size k, given up to translation (its k-deck). Results of Alon, Caro, Krasikov, and Roditty [1] show that this is possible provided k > log 2 n. Mnukhin [10] showed that every subset of Z n of size k is reconstructible from its (k − 1)-deck, provided k ≥ 4. We show ...
متن کاملHurewicz Sets of Reals without Perfect Subsets
We show that even for subsetsX of the real line which do not contain perfect sets, the Hurewicz property does not imply the property S1(Γ,Γ), asserting that for each countable family of open γ-covers of X , there is a choice function whose image is a γcover of X . This settles a problem of Just, Miller, Scheepers, and Szeptycki. Our main result also answers a question of Bartoszyński and the se...
متن کاملDefining Additive Subgroups of the Reals from Convex Subsets
Let G be a subgroup of the additive group of real numbers and let C ⊆ G be infinite and convex in G. We show that G is definable in (R,+, ⋅, C) and that Z is definable if G has finite rank. This has a number of consequences for expansions of certain o-minimal structures on the real field by multiplicative groups of complex numbers. We answer some questions about expansions of o-minimal structur...
متن کاملSpecial Subsets of the Reals and Tree Forcing Notions
We study relationships between classes of special subsets of the reals (e.g. meager-additive sets, γ-sets, C′′-sets, λ-sets) and the ideals related to the forcing notions of Laver, Mathias, Miller and Silver.
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 1999
ISSN: 1077-8926
DOI: 10.37236/1452