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Vector sets with no repeated differences

Péter Komjáth (1993)

Colloquium Mathematicae

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 2 , “not” if the set is allowed to be of size ( 2 2 0 ) + . It is consistent that the continuum is large, but the statement still holds for every set smaller than continuum.

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