On structural completeness of implicational logics

Studia Logica 50 (2):275 - 297 (1991)
We consider the notion of structural completeness with respect to arbitrary (finitary and/or infinitary) inferential rules. Our main task is to characterize structurally complete intermediate logics. We prove that the structurally complete extension of any pure implicational in termediate logic C can be given as an extension of C with a certain family of schematically denned infinitary rules; the same rules are used for each C. The cardinality of the family is continuum and, in the case of (the pure implicational fragment of) intuitionistic logic, the family cannot be reduced to a countable one. It means that the structurally complete extension of the intuitionistic logic is not countably axiomatizable by schematic rules.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1007/BF00370188
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 22,660
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA

Add more references

Citations of this work BETA
Lloyd Humberstone (2000). Contra-Classical Logics. Australasian Journal of Philosophy 78 (4):438 – 474.

Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

9 ( #393,699 of 1,938,828 )

Recent downloads (6 months)

1 ( #459,264 of 1,938,828 )

How can I increase my downloads?

My notes
Sign in to use this feature

Start a new thread
There  are no threads in this forum
Nothing in this forum yet.