Document Type

Article

Publication Date

12-2015

Publication Title

The Journal of Symbolic Logic

Abstract

We prove that the statement "there is a k such that for every f there is a k-bounded diagonally non-recursive function relative to f" does not imply weak K\"onig's lemma over RCA0+BΣ02. This answers a question posed by Simpson. A recursion-theoretic consequence is that the classic fact that every k-bounded diagonally non-recursive function computes a 2-bounded diagonally non-recursive function may fail in the absence of IΣ02.

DOI

10.1017/jsl.2015.43

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