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- W4299513667 abstract "We prove upper and lower bounds on the effective content and logical strength for a variety of natural restrictions of Hindman's Finite Sums Theorem. For example, we show that Hindman's Theorem for sums of length at most 2 and 4 colors implies $mathsf{ACA}_0$. An emerging {em leitmotiv} is that the known lower bounds for Hindman's Theorem and for its restriction to sums of at most 2 elements are already valid for a number of restricted versions which have simple proofs and better computability- and proof-theoretic upper bounds than the known upper bound for the full version of the theorem. We highlight the role of a sparsity-like condition on the solution set, which we call apartness." @default.
- W4299513667 created "2022-10-02" @default.
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- W4299513667 date "2017-01-21" @default.
- W4299513667 modified "2023-10-18" @default.
- W4299513667 title "New bounds on the strength of some restrictions of Hindman's Theorem" @default.
- W4299513667 doi "https://doi.org/10.48550/arxiv.1701.06095" @default.
- W4299513667 hasPublicationYear "2017" @default.
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