A note on the independence of premiss rule

&
Mathematical Logic Quarterly 62 (1-2):72-76 (2016)
  Copy   BIBTEX

Abstract

In this note, we prove that certain theories of (many‐sorted) intuitionistic predicate logic are closed under the independence of premiss rule (IPR). As corollaries, we show that and extended by some non‐classical axioms and non‐constructive axioms are closed under IPR.

Categories

Add categories

Keywords

Reprint years

DOI

10.1002/malq.201500032

Other Versions

No versions found

Links

PhilArchive

    This entry is not archived by us. If you are the author and have permission from the publisher, we recommend that you archive it. Many publishers automatically grant permission to authors to archive pre-prints. By uploading a copy of your work, you will enable us to better index it, making it easier to find.

    Upload a copy of this work     Papers currently archived: 105,170

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

On the independence of premiss axiom and rule.Hajime Ishihara & Takako Nemoto - 2020 - Archive for Mathematical Logic 59 (7-8):793-815.
Analyticity, Balance and Non-admissibility of Cut in Stoic Logic.Susanne Bobzien & Roy Dyckhoff - 2018 - Studia Logica 107 (2):375-397.
The Friedman‐Translation for Martin‐Löf's Type Theory.Erik Palmgren - 1995 - Mathematical Logic Quarterly 41 (3):314-326.
The McKinsey–Lemmon logic is barely canonical.Robert Goldblatt & Ian Hodkinson - 2007 - Australasian Journal of Logic 5:1-19.
Markov's Rule revisited.Daniel Leivant - 1990 - Archive for Mathematical Logic 30 (2):125-127.
Classically archetypal rules.Tomasz Połacik & Lloyd Humberstone - 2018 - Review of Symbolic Logic 11 (2):279-294.
Co-theory of sorted profinite groups for PAC structures.Daniel Max Hoffmann & Junguk Lee - 2023 - Journal of Mathematical Logic 23 (3).
An Intuitionistic Axiomatisation of Real Closed Fields.Erik Palmgren - 2002 - Mathematical Logic Quarterly 48 (2):297-299.
Completeness and incompleteness for intuitionistic logic.Charles Mccarty - 2008 - Journal of Symbolic Logic 73 (4):1315-1327.
Some weak fragments of {${\rm HA}$} and certain closure properties.Morteza Moniri & Mojtaba Moniri - 2002 - Journal of Symbolic Logic 67 (1):91-103.

Analytics

Added to PP
2016-02-04

Downloads
47 (#520,319)

6 months
8 (#528,816)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Conservation as Translation.Giulio Fellin & Peter Schuster - forthcoming - Review of Symbolic Logic:1-33.
On the independence of premiss axiom and rule.Hajime Ishihara & Takako Nemoto - 2020 - Archive for Mathematical Logic 59 (7-8):793-815.

Add more citations

References found in this work

Syntactic translations and provably recursive functions.Daniel Leivant - 1985 - Journal of Symbolic Logic 50 (3):682-688.
Some principles weaker than Markov’s principle.Makoto Fujiwara, Hajime Ishihara & Takako Nemoto - 2015 - Archive for Mathematical Logic 54 (7-8):861-870.
A Note on the Godel-Gentzen Translation.Hajime Ishihara - 2000 - Mathematical Logic Quarterly 46 (1):135-138.

Add more references