منابع مشابه
Hamel bases and well–ordering the continuum
In ZF, the existence of a Hamel basis does not yield a well–ordering of R. Throughout this paper, by a Hamel basis we always mean a basis for R, construed as a vector space over Q. We denote by E the Vitali equivalence relation, xEy iff x− y ∈ Q for x, y ∈ R. We also write [x]E = {y : yEx} for the E–equivalence class of x. A transversal for the set of all E–equivalence classes picks exactly one...
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In the paper we prove that axiom CPA prism, which follows from the Covering Property Axiom CPA and holds in the iterated perfect set model, implies that there exists a Hamel basis which is a union of less than continuum many pairwise disjoint perfect sets. We will also give two consequences of this last fact. 1 The result and its consequences In this paper we will use standard set theoretic ter...
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Let A be an asymptotic basis for N0 of some order. By an essentiality of A one means a subset P such that A\P is no longer an asymptotic basis of any order and such that P is minimal among all subsets of A with this property. A finite essentiality of A is called an essential subset. In a recent paper, Deschamps and Farhi asked the following two questions : (i) does every asymptotic basis of N0 ...
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We study the problem of removing an element from an additive basis in a general abelian group. We introduce analogues of the classical functions X,S and E (defined in the case of N) and obtain bounds on them. Our estimates on the functions SG and EG are valid for general abelian groups G while in the case of XG we show that distinct types of behaviours may occur depending on G.
متن کاملOn Additive Bases
The critical number of G, denoted by c(G), is the smallest s such that Σ(S) = G for every subset S of G with cardinality s not containing 0. The parameter c(G) was first studied by Erdős and Heilbronn in [4]. They obtained the inequality c(Zp) ≤ 3 √ 6p. Olson proved in [13] that c(Zp) ≤ √ 4p− 3 + 1. The authors of [1] obtained the inequality c(Zp) ≤ √ 4p− 7. The evaluation of c(G) for groups wi...
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ژورنال
عنوان ژورنال: Aequationes mathematicae
سال: 2013
ISSN: 0001-9054,1420-8903
DOI: 10.1007/s00010-013-0241-7