Iterated jump noncomputability and compactness

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 Kőnig’s lemma (WWKL), and weak Kőnig’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.