Stone-type duality theorems, which relate algebraic and relational/topological models, are important tools in logic because — in addition to elegant abstraction — they strengthen soundness and completeness to a categorical equivalence, yielding a framework through which both algebraic and topological methods can be brought to bear on a logic. We give a systematic treatment of Stone-type duality...

introduction & objective: after urinary tract infection and prostatic disorders , the urine stones are the third common genitourinary diseases. demographic, environmental and genetic factors affect urine stone formation. the aim of our study is to survey epidemiologic factors in patients with urinary stones referring to educational hospitals of hamadan during 2010-2013.      materials & methods...

We introduce an endofunctor H on the category baℓ of bounded archimedean ℓ-algebras and show that there is a dual adjunction between Alg(H) algebras for Coalg(V) coalgebras Vietoris V compact Hausdorff spaces. prove Gelfand duality lifts to equivalence full reflective subcategory Algu(H) Alg(H). provide alternate view by introducing Hu consisting uniformly complete objects showing Alg(Hu) isomo...

A systematic theory of structural limits for finite models has been developed by Nesetril and Ossona de Mendez. It is based on the insight that collection structures can be embedded, via a map they call Stone pairing, in space measures, where desired computed. We show closely related but finer grained (finitely additive) measures arises -- Stone-Priestley duality notion types from model enrichi...

We study countable saturation of metric reduced products and introduce continuous fields of metric structures indexed by locally compact, separable, completely metrizable spaces. Saturation of the reduced product depends both on the underlying index space and the model. By using the Gelfand–Naimark duality we conclude that the assertion “Stone–Čech remainder of the half-line has only trivial au...

in this work, the waste stone sludge obtained from the granite and marble stone processing factories was used for the manufacture of artificial stones using vibratory compaction in a vacuum environment. the results obtained showed that water absorption and density increased, and the flexure, compressive, and tensile strengths decreased with increase in the content of the waste stone sludge. the...

The term Stone-type duality often refers to a dual equivalence between category of lattices or other partially ordered structures on one side and topological the other. This paper is part larger endeavour that aims extend web dualities from metric and, more generally, quantale-enriched categories. In particular, we improve our previous work show how certain results for categories [ 0 , 1 ] -enr...

in this paper, we try to determine the status of the relation between dahr world and matrial world. the conclusion shows the subjective duality and objective unity of dahr and material entities. two interpretations of this duality can be suggested. in the first interpretation, this unity, and the duality supposed, are explained on the basis of different intellectual cognition of immaterial and ...

A partial ordering P has the property SEP (or SEP(P )), if, for a sufficiently large regular cardinal χ, the family of elementary submodels of H(χ) of cardinality א1 with the property that [M ]א0 ∩M is cofinal subset (with respect to ⊆) of [M ]א0 and P ∩M ≤σ P , is cofinal (also with respect to ⊆) in [H(χ)]א1 (see Proposition 2 below). We describe, in section 1, against which historical backgro...