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INTERRELATION BETWEEN WEAK FRAGMENTS OF DOUBLE NEGATION SHIFT AND RELATED PRINCIPLES

Published online by Cambridge University Press:  23 October 2018

MAKOTO FUJIWARA  and
ULRICH KOHLENBACH
MAKOTO FUJIWARA
Affiliation:
WASEDA INSTITUTE FOR ADVANCED STUDY WASEDA UNIVERSITY 1-6-1 NISHI WASEDA, SHINJUKU-KU TOKYO 169-8050, JAPANE-mail: makoto_fujiwara@aoni.waseda.jp
ULRICH KOHLENBACH
Affiliation:
FACHBEREICH MATHEMATIK TU DARMSTADT SCHLOSSGARTENSTRASSE 7 D-64289 DARMSTADT, GERMANYE-mail: kohlenbach@mathematik.tu-darmstadt.de
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Abstract

We investigate two weak fragments of the double negation shift schema, which are motivated, respectively, from Spector’s consistency proof of ACA0 and from the negative translation of RCA0, as well as double negated variants of logical principles. Their interrelations over both intuitionistic arithmetic and analysis are completely solved.

Keywords

03B2003F5003F1003F25double negation shiftfragments of classical logicintuitionistic arithmetic and analysis
Type
Articles
Information
The Journal of Symbolic Logic , Volume 83 , Issue 3 , September 2018 , pp. 991 - 1012
Copyright
Copyright © The Association for Symbolic Logic 2018 

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