The De Morgan Medal

The Ramanujan Journal -     

De Morgan classifying toposes

We present a general method for deciding whether a Grothendieck topos satisfies De Morgan's law (resp. the law of excluded middle) or not; applications to the theory of classifying toposes follow. Specifically, we obtain a syntactic characterization of the class of geometric theories whose classifying toposes satisfy De Morgan's law (resp. are Boolean), as well as model-theoretic criteria for theories whose classifying toposes arise as localizations of a given presheaf topos.     

Free De Morgan Bisemigroups and Bisemilattices

We give a geometric representation of free De Morgan bisemigroups, free commutative De Morgan bisemigroups, and free De Morgan bisemilattices by using labeled graphs.2000 Mathematics Subject Classification: 08A70, 08B20This research was supported by the National Foundation of Scientific Research of Hungary under grant no. T30511.     

Relating De Morgan triples with Atanassov’s intuitionistic De Morgan triples via automorphisms

In this paper the relation between De Morgan triples on the unit interval and Atanassov’s intuitionistic De Morgan triples is presented, showing how to obtain, in a canonical way, Atanassov’s intuitionistic De Morgan triples from De Morgan triples. Moreover, we also show that the automorphisms on the unit interval and on L∗ (the intuitionistic value lattice) are in one-to-one correspondence and how automorphisms on L∗ act on Atanassov’s intuitionistic De Morgan triples. It is also proved that the action of automorphisms and the canonical construction of De Morgan triples on L∗ commutes.     

德摩根代数一个可拟一致化的充要条件

给出德摩根双拓扑代数(L，Q，τ，σ)可拟一致化的一个充要条件。     

Functorial Duality for Ortholattices and De Morgan Lattices

Relational semantics for nonclassical logics lead straightforwardly to topological representation theorems of their algebras. Ortholattices and De Morgan lattices are reducts of the algebras of various nonclassical logics. We define three new classes of topological spaces so that the lattice categories and the corresponding categories of topological spaces turn out to be dually isomorphic. A key feature of all these topological spaces is that they are ordered relational or ordered product topologies.     

德摩根一致代数的完备性

本文建立了几个德摩根一致代数是完备的充分必要条件,它包括了经典的相应结果作为特例并且提供了相应的模糊模式     

德摩根一致代数的度量化

我们给出了德摩根一致代数可伪度量化的一个充分必要条件。     

Congruence properties of pseudocomplemented De Morgan algebras

In this paper we first describe the Priestley duality for pseudocomplemented De Morgan algebras by combining the known dualities of distributive p‐algebras due to Priestley and for De Morgan algebras due to Cornish and Fowler. We then use it to characterize congruence‐permutability, principal join property, and the property of having only principal congruences for pseudocomplemented De Morgan algebras. The congruence‐uniform pseudocomplemented De Morgan algebras are also described.     

Unification and Projectivity in De Morgan and Kleene Algebras

We provide a complete classification of solvable instances of the equational unification problem over De Morgan and Kleene algebras with respect to unification type. The key tool is a combinatorial characterization of finitely generated projective De Morgan and Kleene algebras.     

德摩根拓扑代数可度量化的一个充分条件

得出德摩根拓扑代数可度量化的一个充分条件 ,其结果将经典 Urysohn度量化定理以及模糊度量化定理作为其特例     

强De Morgan代数上的广义R0 t-模

在De Morgan代数上引入广义R0算子,举例说明了一般De Morgan代数中的广义R0算子不能构成t-模。引入强De Morgan代数的概念,讨论它的基本性质,证明强De Morgan代数L上的广义R0算子构成t-模(称为广义R0t-模)。给出若干重要反例,并证明强De Morgan代数上的广义R0t-模是左连续的。     

德摩根拓扑代数的局部紧

利用德摩根子代数概念以及紧性引进了德摩根拓扑代数的局部紧,研究了它与分离公理之间的关系,并给出了一个类似于Ｂａｉｒｅ 范畴定理的定理。所有结果包括了经典的相应结果作为特例,并且提供了相应的模糊模式