## Vector sets with no repeated differences

### Volume 64 / 1993

Colloquium Mathematicum 64 (1993), 129-134
DOI: 10.4064/cm-64-1-129-134

#### 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.