The second Committee Draft of the ISO standard \Z Nota-tion" is expected to be published soon after the ZUM'98 proceedings. This paper provides an overview of Standard Z from the perspective of the diierences between its notation and that of Spivey's de facto standard \The Z Notation: A Reference Manual". Its aim is to make the diierences be more widely known and hence enable wider exploitation...

We define topological and analytic indices in R/Z K-theory and show that they are equal.

The problem of reassembling an object from its parts or fragments has never been addressed with a unified computational approach, which depends on the pure geometric form of the parts and not application-specific features. We propose a method for the automatic reconstruction of a model based on the geometry of its parts, which may be computergenerated models or range-scanned models. The matchin...

Let p be a prime number. In this article we present a theorem, suggested by Peter Scholze, which states that Gal(Qp/Qp) is the étale fundamental group of a certain object Z which is defined over an algebraically closed field. This object is the quotient of the “punctured perfectoid open disk” by an action of the group Qp . The proof of this fact combines two themes: the tilting equivalence for ...

The use of Geometric Logic as the foundation of a speciication language called GeoZ is proposed elsewhere 4]. In this note we explore GeoZ from the perspective of practitioners, who are familiar with the existing Z notation, by explaining the issues that arise and the essential role of schema entailment in the GeoZ reformulation of Z's mathematical toolkit.