Vector sets with no repeated differences

• Autorzy: Péter Komjáth
• 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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1993
• Tom: 64
• Numer: 1
• Strony: 129-134

Daty

wydano

1993

otrzymano

1991-06-20

poprawiono

1992-03-03

Twórcy

autor

Péter Komjáth

• 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.