A Schnorr test relative to some oracle A may informally be called “universal” if it covers all Schnorr tests. Since no true universal Schnorr test exists, such an A cannot be computable. We prove that the sets with this property are exactly those with high Turing degree. Our method is closely related to the proof of Terwijn and Zambella’s characterization of the oracles which are low for Schnorr tests. We also consider the oracles which compute relativized Schnorr tests with the (...) weaker property of covering all computable reals. The degrees of these oracles strictly include the hyperimmune degrees and are strictly included in the degrees not computably traceable. (shrink)

Recent research about the microbiome points to a picture in which we, humans, are ‘living through’ nature, and nature itself is living in us. Our bodies are hosting—and depend on—the multiple species that constitute human microbiota. This article will discuss current research on the microbiome through the ideas of Japanese ecologist Imanishi Kinji (1902–1992). First, some of Imanishi’s key ideas regarding the world of living beings and multispecies societies are presented. Second, seven types of relationships concerning the human microbiome, human (...) beings, and the environment are explored. Third, inspired by Imanishi’s work, this paper develops the idea of dynamic, porous, and complex multispecies societies in which different living beings or species are codependent on others, including microbiota and human beings. (shrink)