# Vector sets with no repeated differences

Colloquium Mathematicae (1993)

- Volume: 64, Issue: 1, page 129-134
- ISSN: 0010-1354

## Access Full Article

top## Abstract

top## How to cite

topKomjáth, Péter. "Vector sets with no repeated differences." Colloquium Mathematicae 64.1 (1993): 129-134. <http://eudml.org/doc/210162>.

@article{Komjáth1993,

abstract = {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.},

author = {Komjáth, Péter},

journal = {Colloquium Mathematicae},

keywords = {combinatorial set theory; forcing; consistency},

language = {eng},

number = {1},

pages = {129-134},

title = {Vector sets with no repeated differences},

url = {http://eudml.org/doc/210162},

volume = {64},

year = {1993},

}

TY - JOUR

AU - Komjáth, Péter

TI - Vector sets with no repeated differences

JO - Colloquium Mathematicae

PY - 1993

VL - 64

IS - 1

SP - 129

EP - 134

AB - 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.

LA - eng

KW - combinatorial set theory; forcing; consistency

UR - http://eudml.org/doc/210162

ER -

## References

top- [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. Zbl0418.04002
- [2] P. Erdős, Some applications of Ramsey's theorem to additive number theory, European J. Combin. 1 (1980), 43-46. Zbl0442.10037
- [3] P. Erdős and S. Kakutani, On non-denumerable graphs, Bull. Amer. Math. Soc. 49 (1943), 457-461. Zbl0063.01275
- [4] P. Erdős and R. Rado, A partition calculus in set theory, ibid. 62 (1956), 427-489. Zbl0071.05105
- [5] D. Fremlin, Consequences of Martin's Axiom, Cambridge University Press, 1984. Zbl0551.03033

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.