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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References found in this work BETA

Finitism.W. W. Tait - 1981 - Journal of Philosophy 78 (9):524-546.
Partial Realizations of Hilbert's Program.Stephen G. Simpson - 1988 - Journal of Symbolic Logic 53 (2):349-363.
Fragments of Arithmetic.Wilfried Sieg - 1985 - Annals of Pure and Applied Logic 28 (1):33-71.

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