Hindman's theorem does not code ∅^(ω) in one application

2026/07/20 by Lu Liu, Ludovic Patey
#math.LO #math.CO

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Abstract

We prove that for every non-arithmetic set~C and every arithmetic finite coloring of~ℕ, there is an infinite set H ⊆ ℕ whose non-empty finite sums of distinct elements is monochromatic, and C is not H-computable. We also study restrictions of Hindman's theorem to simple colorings.

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