Resumen de IP sets, Hilbert cubes

Norbert Hegyvári

• Given a subset E of the set of natural numbers, FS(E) is de¯ned as the collection of all sums of elements of ¯nite subsets of E and any translation of FS(E) is said to be a Hilbert cube. We estimate the rate of growth of E given that FS(E) avoids a set of multiplies of a given in¯nite set of primes. The results are related to a result which states that there exists an in¯nite Hibert cube contained in the set of square-free numbers.