Hilbert versus Hindman

Archive for Mathematical Logic 51 (1-2):123-125 (2012)

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
Keywords Reverse mathematics  Pigeonhole  Conservation  Finitism
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DOI 10.1007/s00153-011-0257-4
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