%0 Journal Article
%J The Journal of Symbolic Logic
%D 2018
%T Truncation and Semi-Decidability Notions in Applicative Theories
%A Gerhard Jäger
%A Timtej Rosebrock
%A Kentaro Sato
%X BON+ 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 .
%B The Journal of Symbolic Logic
%V 83
%P 967-990
%G eng
%U http://www.iam.unibe.ch/ltgpub/2016/jarosa16.pdf
%N 03
%R 10.7892/boris.125568