Folkman's theorem states that ifA={a1< a2<···} satisfyingA (n)> n1/2+ ϵ, whereA (n)=∑ ai≤
n1), thenP (A)={ai1+ ai2+···+ ais: i1< i2<···< is; s∈ N; aij∈ A} contains an infinite arithmetic …

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Folkman's theorem states that ifA={a 1< a 2<...} satisfyingA (n)> n 1/2+ ε, whereA (n)= ai=< n
1), thenP (A)={ai 1+ ai 2+...+ ais: i 1< i 2<...< is; s N; aij A} contains an infinite arithmetic …