Pretabular varieties of modal algebras

Studia Logica 39 (2-3):101 - 124 (1980)
Abstract
We study modal logics in the setting of varieties of modal algebras. Any variety of modal algebras generated by a finite algebra — such, a variety is called tabular — has only finitely many subvarieties, i.e. is of finite height. The converse does not hold in general. It is shown that the converse does hold in the lattice of varieties of K4-algebras. Hence the lower part of this lattice consists of tabular varieties only. We proceed to show that there is a continuum of pretabular varieties of K4-algebras — those are the non-tabular varieties all of whose proper subvarieties are tabular — in contrast with Maksimova's result that there are only five pretabular varieties of S4-algebras.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1007/BF00370315
Options
 Save to my reading list
Follow the author(s)
Edit this record
My bibliography
Export citation
Find it on Scholar
Mark as duplicate
Request removal from index
Revision history
Download options
Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 32,628
Through your library
References found in this work BETA
Some Embedding Theorems for Modal Logic.David Makinson - 1971 - Notre Dame Journal of Formal Logic 12 (2):252-254.
Five Critical Modal Systems.L. Esakia & V. Meskhi - 1977 - Theoria 43 (1):52-60.

Add more references

Citations of this work BETA
The Structure of Lattices of Subframe Logics.Frank Wolter - 1997 - Annals of Pure and Applied Logic 86 (1):47-100.
Willem Blok and Modal Logic.W. Rautenberg, M. Zakharyaschev & F. Wolter - 2006 - Studia Logica 83 (1-3):15-30.
Algebraic Semantics for Quasi-Classical Modal Logics.W. J. Blok & P. Köhler - 1983 - Journal of Symbolic Logic 48 (4):941-964.

View all 13 citations / Add more citations

Similar books and articles
Added to PP index
2009-01-28

Total downloads
30 ( #196,717 of 2,236,067 )

Recent downloads (6 months)
2 ( #267,602 of 2,236,067 )

How can I increase my downloads?

Monthly downloads
My notes
Sign in to use this feature