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TRUNCATION AND SEMI-DECIDABILITY NOTIONS IN APPLICATIVE THEORIES

Published online by Cambridge University Press:  23 October 2018

GERHARD JÄGER ,
TIMOTEJ ROSEBROCK  and
SATO KENTARO
GERHARD JÄGER
Affiliation:
INSTITUTE OF COMPUTER SCIENCE UNIVERSITY OF BERN NEUBRÜCKSTRASSE 10, 3012BERN, SWITZERLAND E-mail: jaeger@inf.unibe.ch
TIMOTEJ ROSEBROCK
Affiliation:
INSTITUTE OF COMPUTER SCIENCE UNIVERSITY OF BERN NEUBRÜCKSTRASSE 10, 3012BERN, SWITZERLAND E-mail: rose@inf.unibe.ch
SATO KENTARO
Affiliation:
INSTITUTE OF COMPUTER SCIENCE UNIVERSITY OF BERN NEUBRÜCKSTRASSE 10, 3012BERN, SWITZERLAND E-mail: sato@inf.unibe.ch
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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.

Keywords

03B4003D2503D7503E1503F99applicative theoriesexplicit mathematicsabstract computability(semi-) decidabilityKleene’s second modelgraph modelHausdorff–Kuratowski difference hierarchy
Type
Articles
Information
The Journal of Symbolic Logic , Volume 83 , Issue 3 , September 2018 , pp. 967 - 990
Copyright
Copyright © The Association for Symbolic Logic 2018 

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