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Erdős problem 1023

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Let F(n)F(n) be the maximal size of a family of subsets of {1,…,n}\{1,\ldots,n\} such that no set in this family is the union of other members of the family. Is it true that there is a constant c>0c>0 such that F(n)∼c2nn1/2?F(n)\sim c \frac{2^n}{n^{1/2}}?

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