Details

Autor(en) / Beteiligte

• JÄGER, GERHARD
• ROSEBROCK, TIMOTEJ
• KENTARO, SATO

Titel

TRUNCATION AND SEMI-DECIDABILITY NOTIONS IN APPLICATIVE THEORIES

Ist Teil von

• The Journal of symbolic logic, 2018-09, Vol.83 (3), p.967-990

Ort / Verlag

Pasadena: Association for Symbolic Logic, Inc

Erscheinungsjahr

2018

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• 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.