Totality in Applicative Theories (1995)
| Venue: | ANNALS OF PURE AND APPLIED LOGIC |
| Citations: | 19 - 11 self |
BibTeX
@INPROCEEDINGS{Jäger95totalityin,
author = {Gerhard Jäger and Thomas Strahm},
title = {Totality in Applicative Theories},
booktitle = {ANNALS OF PURE AND APPLIED LOGIC},
year = {1995},
pages = {83--92},
publisher = {Kluwer}
}
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Abstract
In this paper we study applicative theories of operations and numbers with (and without) the non-constructive minimum operator in the context of a total application operation. We determine the proof-theoretic strength of such theories by relating them to well-known systems like Peano Arithmetic PA and the system (\Pi 0 1 -CA) !"0 of second order arithmetic. Essential use will be made of so-called fixed-point theories with ordinals, certain infinitary term models and Church Rosser properties.
