Counting the maximal intermediate constructive logics

Journal of Symbolic Logic 58 (4):1365-1401 (1993)
Abstract
A proof is given that the set of maximal intermediate propositional logics with the disjunction property and the set of maximal intermediate predicate logics with the disjunction property and the explicit definability property have the power of continuum. To prove our results, we introduce various notions which might be interesting by themselves. In particular, we illustrate a method to generate wide sets of pairwise "constructively incompatible constructive logics". We use a notion of "semiconstructive" logic and define wide sets of "constructive" logics by representing the "constructive" logics as "limits" of decreasing sequences of "semiconstructive" logics. Also, we introduce some generalizations of the usual filtration techniques for propositional logics. For instance, "filtrations over rank formulas" are used to show that any two different logics belonging to a suitable uncountable set of "constructive" logics are "constructively incompatible"
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2307/2275149
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 33,723
Through your library

References found in this work BETA

Superconstructive Propositional Calculi with Extra Axiom Schemes Containing One Variable.J. G. Anderson - 1972 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 18 (8-11):113-130.
A Result on Propositional Logics Having the Disjunction Property.Robert E. Kirk - 1982 - Notre Dame Journal of Formal Logic 23 (1):71-74.

Add more references

Citations of this work BETA

Add more citations

Similar books and articles

Analytics

Added to PP index
2009-01-28

Total downloads
202 ( #25,312 of 2,261,413 )

Recent downloads (6 months)
1 ( #385,489 of 2,261,413 )

How can I increase my downloads?

Monthly downloads

My notes

Sign in to use this feature