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Hilbert versus Hindman
Archive for Mathematical Logic 51 (1-2):123-125 (2012)
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.My notes
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Citations of this work
A weak variant of Hindman’s Theorem stronger than Hilbert’s Theorem.Lorenzo Carlucci - 2018 - Archive for Mathematical Logic 57 (3-4):381-389.
Linear extensions of partial orders and reverse mathematics.Emanuele Frittaion & Alberto Marcone - 2012 - Mathematical Logic Quarterly 58 (6):417-423.
Hindman’s theorem for sums along the full binary tree, $$\Sigma ^0_2$$ Σ 2 0 -induction and the Pigeonhole principle for trees. [REVIEW]Daniele Tavernelli & Lorenzo Carlucci - 2022 - Archive for Mathematical Logic 61 (5-6):827-839.
Hindman’s theorem for sums along the full binary tree, $$\Sigma ^0_2$$ Σ 2 0 -induction and the Pigeonhole principle for trees. [REVIEW]Lorenzo Carlucci & Daniele Tavernelli - 2022 - Archive for Mathematical Logic 61 (5):827-839.
References found in this work
Partial realizations of Hilbert's program.Stephen G. Simpson - 1988 - Journal of Symbolic Logic 53 (2):349-363.
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