Truncation and Semi-Decidability Notions in Applicative Theories

TitleTruncation and Semi-Decidability Notions in Applicative Theories
Publication TypeJournal Article
Year of Publication2018
AuthorsJäger, G, Rosebrock, T, Sato, K
JournalThe Journal of Symbolic Logic
AbstractBON+ is an applicative theory and closely related to the first order parts of the standard systems of explicit mathematics. As such it is also a natural framework for abstract computations. In this article we analyze this aspect of BON+ more closely. First a point is made for introducing a new operation τN , called truncation, to obtain a natural formalization of partial recursive functions in our applicative framework. Then we introduce the operational versions of a series of notions that are all equivalent to semi- decidability in ordinary recursion theory on the natural numbers, and study their mutual relationships over BON+ with τN .