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- Publisher
- Springer Journals
- Copyright
- Copyright © 2015 by Springer-Verlag Berlin Heidelberg
- Subject
- Mathematics; Mathematical Logic and Foundations; Mathematics, general; Algebra
- ISSN
- 0933-5846
- eISSN
- 1432-0665
- DOI
- 10.1007/s00153-015-0448-5
- Publisher site
- See Article on Publisher Site
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 (h-DNR) implies Ramsey-type weak König’s lemma (RWKL). In this paper, we prove that for every computable order h, there exists an $${\omega}$$ ω -model of h-DNR which is not a not model of the Ramsey-type graph coloring principle for two colors (RCOLOR 2) 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 $${\omega}$$ ω -models.
Journal
Archive for Mathematical Logic – Springer Journals
Published: Sep 21, 2015