Iterated jump noncomputability and compactness
Logic
2025-09-18 v4
Abstract
We use reverse mathematics to analyze "iterated jump" versions of the following four principles: the atomic model theorem with subenumerable types (AST), the diagonally noncomputable principle (DNR), weak weak K\H{o}nig's lemma (WWKL), and weak K\H{o}nig's lemma (WKL). The logical relationships between these principles are summarized in Figure 1 and include, among other things, an infinite chain and an infinite antichain, the latter of which represents a strong form of non-linearity in terms of provability strength among "natural" combinatorial principles.
Keywords
Cite
@article{arxiv.2506.20620,
title = {Iterated jump noncomputability and compactness},
author = {Gavin Dooley},
journal= {arXiv preprint arXiv:2506.20620},
year = {2025}
}
Comments
14 pages, 2 figures. Feedback welcome. Various changes made to the previous version, including a more unified (and more correct) presentation of the main proofs