Graduate studies at Western
Studia Logica 64 (2):215-256 (2000)
|Abstract||This paper is the concluding part of  and , and it investigates the inner structure of the lattice (MHA) of all varieties of monadic Heyting algebras. For every n , we introduce and investigate varieties of depth n and cluster n, and present two partitions of (MHA), into varieties of depth n, and into varieties of cluster n. We pay a special attention to the lower part of (MHA) and investigate finite and critical varieties of monadic Heyting algebras in detail. In particular, we prove that there exist exactly thirteen critical varieties in (MHA) and that it is decidable whether a given variety of monadic Heyting algebras is finite or not. The representation of (MHA) is also given. All these provide us with a satisfactory insight into (MHA). Since (MHA) is dual to the lattice NExtMIPC of all normal extensions of the intuitionistic modal logic MIPC, we also obtain a clearer picture of the lattice structure of intuitionistic modal logics over MIPC.|
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
|Through your library||Configure|
Similar books and articles
H. P. Sankappanavar (2011). Expansions of Semi-Heyting Algebras I: Discriminator Varieties. Studia Logica 98 (1-2):27-81.
Andrzej Sendlewski (1995). Axiomatic Extensions of the Constructive Logic with Strong Negation and the Disjunction Property. Studia Logica 55 (3):377 - 388.
Hector Gramaglia & Diego Vaggione (1996). Birkhoff-Like Sheaf Representation for Varieties of Lattice Expansions. Studia Logica 56 (1-2):111 - 131.
Renato A. Lewin (1987). Interpretations Into Monadic Algebras. Studia Logica 46 (4):329 - 342.
B. A. Davey & H. A. Priestley (1996). Optimal Natural Dualities for Varieties of Heyting Algebras. Studia Logica 56 (1-2):67 - 96.
M. Abad, J. P. Díaz Varela, L. A. Rueda & A. M. Suardíaz (2000). Varieties of Three-Valued Heyting Algebras with a Quantifier. Studia Logica 65 (2):181-198.
W. J. Blok (1980). Pretabular Varieties of Modal Algebras. Studia Logica 39 (2-3):101 - 124.
Katarzyna Idziak & Pawel M. Idziak (1988). Decidability Problem for Finite Heyting Algebras. Journal of Symbolic Logic 53 (3):729-735.
Guram Bezhanishvili (1999). Varieties of Monadic Heyting Algebras Part II: Duality Theory. Studia Logica 62 (1):21-48.
Guram Bezhanishvili (1998). Varieties of Monadic Heyting Algebras. Part I. Studia Logica 61 (3):367-402.
Added to index2009-01-28
Total downloads4 ( #189,403 of 738,617 )
Recent downloads (6 months)1 ( #61,778 of 738,617 )
How can I increase my downloads?