Abstract
We show that a statement HIL, which is motivated by a lemma of Hilbert and close in formulation to Hindman’s theorem, is actually much weaker than Hindman’s theorem. In particular, HIL is finitistically reducible in the sense of Hilbert’s program, while Hindman’s theorem is not.
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Hirst, J.L. Hilbert versus Hindman. Arch. Math. Logic 51, 123–125 (2012). https://doi.org/10.1007/s00153-011-0257-4
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DOI: https://doi.org/10.1007/s00153-011-0257-4