| Title | Truncation and Semi-Decidability Notions in Applicative Theories |
| Publication Type | Journal Article |
| Year of Publication | In Press |
| Authors | Jäger, G, Rosebrock, T, Sato, K |
| Journal | The Journal of Symbolic Logic |
| Abstract | 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 . |
| URL | http://www.iam.unibe.ch/ltgpub/2016/jarosa16.pdf |
