Expansions of Semi-Heyting Algebras I: Discriminator Varieties

Studia Logica 98 (1-2):27-81 (2011)
This paper is a contribution toward developing a theory of expansions of semi-Heyting algebras. It grew out of an attempt to settle a conjecture we had made in 1987. Firstly, we unify and extend strikingly similar results of [ 48 ] and [ 50 ] to the (new) equational class DHMSH of dually hemimorphic semi-Heyting algebras, or to its subvariety BDQDSH of blended dual quasi-De Morgan semi-Heyting algebras, thus settling the conjecture. Secondly, we give a criterion for a unary expansion of semi-Heyting algebras to be a discriminator variety and give an algorithm to produce discriminator varieties. We then apply the criterion to exhibit an increasing sequence of discriminator subvarieties of BDQDSH . We also use it to prove that the variety DQSSH of dually quasi-Stone semi- Heyting algebras is a discriminator variety. Thirdly, we investigate a binary expansion of semi-Heyting algebras, namely the variety DblSH of double semi-Heyting algebras by characterizing its simples, and use the characterization to present an increasing sequence of discriminator subvarieties of DblSH . Finally, we apply these results to give bases for “small” subvarieties of BDQDSH , DQSSH , and DblSH
Keywords Dually hemimorphic semi-Heyting algebra  Dually pseudocomplemented semi-Heyting algebra  De Morgan semi-Heyting algebra  Blended ∨-De Morgan law  Blended dually quasi-De Morgan semi-Heyting algebra  Blended dually quasi-Stone semi-Heyting algebra  Double semi-Heyting algebra  congruence  normal filter  discriminator variety  simple  directly indecomposable  subdirectly irreducible  equational base
Categories (categorize this paper)
DOI 10.1007/s11225-011-9322-6
 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: 31,334
Through your library
References found in this work BETA
An Algebraic Approach to Non-Classical Logics.Helena Rasiowa - 1974 - Warszawa, Pwn - Polish Scientific Publishers.
Quasi‐Stone Algebras.Nalinaxi H. Sankappanavar & Hanamantagouda P. Sankappanavar - 1993 - Mathematical Logic Quarterly 39 (1):255-268.

View all 20 references / Add more references

Citations of this work BETA
The Semi Heyting–Brouwer Logic.Juan Manuel Cornejo - 2015 - Studia Logica 103 (4):853-875.

Add more citations

Similar books and articles
Decidability Problem for Finite Heyting Algebras.Katarzyna Idziak & Pawel M. Idziak - 1988 - Journal of Symbolic Logic 53 (3):729-735.
Semi-Post Algebras.Nguyen Cat Ho & Helena Rasiowa - 1987 - Studia Logica 46 (2):149 - 160.
Semi-Demorgan Algebras.David Hobby - 1996 - Studia Logica 56 (1-2):151 - 183.
Nelson Algebras Through Heyting Ones: I.Andrzej Sendlewski - 1990 - Studia Logica 49 (1):105-126.
Added to PP index

Total downloads
20 ( #278,356 of 2,225,156 )

Recent downloads (6 months)
1 ( #425,061 of 2,225,156 )

How can I increase my downloads?

Monthly downloads
My notes
Sign in to use this feature