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We show that there exists a recursive coloring function $c$ such that any$\Pi^0_3$ set is not a solution to $c$ for Hindman's theorem. We also show thatthere exists a recursive coloring function $c$ such that any $\Delta^0_3$ setis not a solution to $c$ for Hindman's theorem restricted on sum of at mostthree numbers.

A recursive coloring function without $\Pi_3^0$ solution for Hindman theorem