Geodesic
Vector sets with no repeated differences
Colloquium Mathematicum, Tome 64 (1993) no. 1, pp. 129-134.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/cm-64-1-129-134

Péter Komjáth 1

1 
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Péter Komjáth. Vector sets with no repeated differences. Colloquium Mathematicum, Tome 64 (1993) no. 1, pp. 129-134. doi : 10.4064/cm-64-1-129-134. http://geodesic.mathdoc.fr/articles/10.4064/cm-64-1-129-134/

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