In this article we deal with Glivenko type theorems for intuitionistic modal logics over Prior’s MIPC. We examine the problems which appear in proving Glivenko type theorems when passing from the intuitionistic propositional logic Int to MIPC. As a result we obtain two different versions of Glivenko’s theorem for logics over MIPC. Since MIPC can be thought of as a one-variable fragment of the i...

In this paper, we introduce the notions of Belluce lattice associated with a bounded $BCK$-algebra and reticulation $BCK$-algebra. To do this, first, define operations $curlywedge ,$ $curlyvee $ $sqcup on $BCK$-algebras study some algebraic properties them. Also, for $A$ Zariski topology Spec(A)$ induced $tau _{A,Max(A)}$ $Max(A)$. We prove $(Max(A),tau_{A,Max(A)})$ is compact topological space...

We perform a systematic investigation of Kazhdan’s relative Property (T) for pairs (G,X), G a locally compact group and X any subset. When G is a connected Lie group or a p-adic algebraic group, we provide an explicit characterization of subsets X ⊂ G such that (G,X) has relative Property (T). In order to extend this characterization to lattices Γ ⊂ G, a notion of “resolutions” is introduced, a...

Property does many things-it incentivizes productive activity, facilitates exchange, forms an integral part of individual identity, and shapes communities. But property does something equally fundamental: it communicates. And perhaps the most ubiquitous and important messages that property communicates have to do with relative status, with the material world defining and reinforcing a variety o...

is atomic in nature . Hence, whenever μ is continuous, we have Tn =1 almost surely for all n. This is in stark contrast with the Glivenko-Cantelli norm, which is known to converge to zero almost surely as n --~ oo (by the Glivenko--Cantelli theorem) . If μ is atomic, it is quite obvious that Tn --~ 0 almost surely as n --~ 0. In order for Tn to be small when μ is nonatomic, we should not use th...