INTERRELATION BETWEEN WEAK FRAGMENTS OF DOUBLE NEGATION SHIFT AND RELATED PRINCIPLES-Reference-Cited by-同舟云学术

INTERRELATION BETWEEN WEAK FRAGMENTS OF DOUBLE NEGATION SHIFT AND RELATED PRINCIPLES

Published:2018-09 Issue:3 Volume:83 Page:991-1012
ISSN:0022-4812
Container-title:The Journal of Symbolic Logic
language:en
Short-container-title:J. symb. log.

Author:

FUJIWARA MAKOTO,KOHLENBACH ULRICH

Abstract

AbstractWe 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.

Publisher

Cambridge University Press (CUP)

Subject

Logic,Philosophy

Reference27 articles.

1. Formal systems for some branches of intuitionistic analysis;Kreisel;Annals of Pure and Applied Logic,1970

2. CONSTRUCTIVE REVERSE MATHEMATICS: COMPACTNESS PROPERTIES

3. Markov's principle, Church's thesis and Lindelöf's theorem

4. Intuitionistic Provability versus Uniform Provability in $$\mathsf{RCA}$$ RCA

5. Classical Consequences of Continuous Choice Principles from Intuitionistic Analysis

Cited by 9 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. EXTENDED FRAMES AND SEPARATIONS OF LOGICAL PRINCIPLES;The Bulletin of Symbolic Logic;2023-07-26

2. On the decomposition of WKL!!;Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences;2023-04-10

3. Refining the arithmetical hierarchy of classical principles;Mathematical Logic Quarterly;2022-06-09

4. $$\Delta ^0_1$$ variants of the law of excluded middle and related principles;Archive for Mathematical Logic;2022-04-29

5. PRENEX NORMAL FORM THEOREMS IN SEMI-CLASSICAL ARITHMETIC;The Journal of Symbolic Logic;2021-06-11