Dorias, FG, Hirst, JL and Shafer, PE orcid.org/0000-0001-5386-9218 (2015) Comparing the strength of diagonally non-recursive functions in the absence of Sigma^0_2 induction. Journal of Symbolic Logic, 80 (4). pp. 1211-1235. ISSN 0022-4812
Abstract
We prove that the statement “there is a k such that for every f there is a k-bounded diagonally nonrecursive function relative to f” does not imply weak König’s lemma over . This answers a question posed by Simpson. A recursion-theoretic consequence is that the classic fact that every k-bounded diagonally nonrecursive function computes a 2-bounded diagonally nonrecursive function may fail in the absence of .
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2015, Association for Symbolic Logic. This is an author produced version of a paper published in Journal of Symbolic Logic. Uploaded in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 24 Feb 2017 12:57 |
Last Modified: | 02 Jul 2017 15:57 |
Published Version: | https://doi.org/10.1017/jsl.2015.43 |
Status: | Published |
Publisher: | Association for Symbolic Logic |
Identification Number: | 10.1017/jsl.2015.43 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:111924 |