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## Colloquium Mathematicum

1993 | 64 | 1 | 129-134
Tytuł artykułu

### Vector sets with no repeated differences

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Treść / Zawartość
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Języki publikacji
EN
Abstrakty
EN
We consider the question when a set in a vector space over the rationals, with no differences occurring more than twice, is the union of countably many sets, none containing a difference twice. The answer is "yes" if the set is of size at most $ℵ_2$, "not" if the set is allowed to be of size $(2^{2^{ℵ_0}})^{+}$. It is consistent that the continuum is large, but the statement still holds for every set smaller than continuum.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
129-134
Opis fizyczny
Daty
wydano
1993
otrzymano
1991-06-20
poprawiono
1992-03-03
Twórcy
autor
• Department of Computer Science, R. Eötvös University, Múzeum Krt. 6-8, 1088 Budapest, Hungary
Bibliografia
• [1] P. Erdős, Set theoretic, measure theoretic, combinatorial, and number theoretic problems concerning point sets in Euclidean space, Real Anal. Exchange 4 (1978-79), 113-138.
• [2] P. Erdős, Some applications of Ramsey's theorem to additive number theory, European J. Combin. 1 (1980), 43-46.
• [3] P. Erdős and S. Kakutani, On non-denumerable graphs, Bull. Amer. Math. Soc. 49 (1943), 457-461.
• [4] P. Erdős and R. Rado, A partition calculus in set theory, ibid. 62 (1956), 427-489.
• [5] D. Fremlin, Consequences of Martin's Axiom, Cambridge University Press, 1984.
Typ dokumentu
Bibliografia
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