The double powerlocale and exponentiation: A case study in geometric logic.
The dual of the category of generalized trees.
The essential cover and the absolute cover of a schematic space
A theorem of Gleason states that every compact space admits a projective cover. More generally, in the category of topological spaces with continuous maps, covers exist with respect to the full subcategory of extremally disconnected spaces. Such a cover of a space is called its absolute. We prove that the absolute exists within the category of schematic spaces, i.e. the spaces underlying a scheme. For a schematic space, we use the absolute to generalize Bourbaki's concept of irreducible component,...
The existence of states on every Archimedean atomic lattice effect algebra with at most five blocks
Effect algebras are very natural logical structures as carriers of probabilities and states. They were introduced for modeling of sets of propositions, properties, questions, or events with fuzziness, uncertainty or unsharpness. Nevertheless, there are effect algebras without any state, and questions about the existence (for non-modular) are still unanswered. We show that every Archimedean atomic lattice effect algebra with at most five blocks (maximal MV-subalgebras) has at least one state, which...
The exocenter of a double Heyting algebra
The frame of fibrewise closed nuclei
The ideal structure of simple ternary algebras
The lattice of bi-numerations of arithmetic. I.
The lattice of bi-numerations of arithmetic. II.
The lattice of equational theories. Part II: The lattice of full sets of terms
The lattice of ideals of a compact semilattice.
The lattice of pseudotopologies on S
The lattice of -subalgebras of a bounded distributive lattice
The MacNeille completion of the poset of partial injective functions.
The maximal semigroup of quotients of a finite semilattice.
The -propositional calculus
T. Almada and J. Vaz de Carvalho (2001) stated the problem to investigate if these Łukasiewicz algebras are algebras of some logic system. In this article an affirmative answer is given and the -propositional calculus, denoted by , is introduced in terms of the binary connectives (implication), (standard implication), (conjunction), (disjunction) and the unary ones (negation) and , (generalized Moisil operators). It is proved that belongs to the class of standard systems of implicative...
The prime and maximal spectra and the reticulation of BL-algebras
In this paper we study the prime and maximal spectra of a BL-algebra, proving that the prime spectrum is a compact T 0 topological space and that the maximal spectrum is a compact Hausdorff topological space. We also define and study the reticulation of a BL-algebra.
The principal join property in demi-p-lattices
The projective spectrum as a distributive lattice
The semigroup of finite complexes of a group