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- W4300554015 abstract "A function is diagonally non-computable (d.n.c.) if it diagonalizes against the universal partial computable function. D.n.c. functions play a central role in algorithmic randomness and reverse mathematics. Flood and Towsner asked for which functions h, the principle stating the existence of an h-bounded d.n.c. function (DNR_h) implies the Ramsey-type Konig's lemma (RWKL). In this paper, we prove that for every computable order h, there exists an~$omega$-model of DNR_h which is not a not model of the Ramsey-type graph coloring principle for two colors (RCOLOR2) and therefore not a model of RWKL. The proof combines bushy tree forcing and a technique introduced by Lerman, Solomon and Towsner to transform a computable non-reducibility into a separation over omega-models." @default.
- W4300554015 created "2022-10-03" @default.
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- W4300554015 date "2014-12-02" @default.
- W4300554015 modified "2023-10-07" @default.
- W4300554015 title "Ramsey-type graph coloring and diagonal non-computability" @default.
- W4300554015 doi "https://doi.org/10.48550/arxiv.1412.0917" @default.
- W4300554015 hasPublicationYear "2014" @default.
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