Review of Symbolic Logic 13 (2):338-374 (2020)

The variety DMM of De Morgan monoids has just four minimal subvarieties. The join-irreducible covers of these atoms in the subvariety lattice of DMM are investigated. One of the two atoms consisting of idempotent algebras has no such cover; the other has just one. The remaining two atoms lack nontrivial idempotent members. They are generated, respectively, by 4-element De Morgan monoids C4 and D4, where C4 is the only nontrivial 0-generated algebra onto which finitely subdirectly irreducible De Morgan monoids may be mapped by noninjective homomorphisms. The homomorphic preimages of C4 within DMM constitute a proper quasivariety, which is shown to have a largest subvariety U. The covers of the variety within U are revealed here. There are just ten of them. In exactly six of these ten varieties, all nontrivial members have C4 as a retract. In the varietal join of those six classes, every subquasivariety is a variety—in fact, every finite subdirectly irreducible algebra is projective. Beyond U, all covers of [or of ] within DMM are discriminator varieties. Of these, we identify infinitely many that are finitely generated, and some that are not. We also prove that there are just 68 minimal quasivarieties of De Morgan monoids.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1017/s1755020318000448
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 59,827
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

The Undecidability of Entailment and Relevant Implication.Alasdair Urquhart - 1984 - Journal of Symbolic Logic 49 (4):1059-1073.
Completeness of Relevant Quantification Theories.Robert K. Meyer, J. Michael Dunn & Hugues Leblanc - 1974 - Notre Dame Journal of Formal Logic 15 (1):97-121.
On Conserving Positive Logics.Robert K. Meyer - 1973 - Notre Dame Journal of Formal Logic 14 (2):224-236.

View all 9 references / Add more references

Citations of this work BETA

Add more citations

Similar books and articles

Varieties Of Tense Algebras.Tomasz Kowalski - 1998 - Reports on Mathematical Logic:53-95.
On Varieties of Biresiduation Algebras.C. J. van Alten - 2006 - Studia Logica 83 (1-3):425-445.
Locally Finite Monoids in Finitely Based Varieties.Edmond W. H. Lee - 2019 - Logic Journal of the IGPL 27 (5):743-745.
On Involutive FL E -Monoids.Sándor Jenei & Hiroakira Ono - 2012 - Archive for Mathematical Logic 51 (7-8):719-738.


Added to PP index

Total views
6 ( #1,083,403 of 2,432,741 )

Recent downloads (6 months)
3 ( #213,901 of 2,432,741 )

How can I increase my downloads?


My notes