It seems fair to say that the connection between sheaves and logic originates with Lawvere
[29]. In generalizing the notion of sheaf to define sheaves over a site (rather than a …

The conceptualization of space is integral to many of the diverse forms of information
systems—for example, the physical space represented in geographical information systems …

The notion of formal space was introduced by Fourman and Grayson [FG] only a few years
ago, but it is only a recent though important step of a long story whose roots involve such …

The existence of the Stone-Tech compactification of a topological space is equivalent,
classically, to the Prime Ideal Theorem, and hence only slightly weaker than the Axiom of …

My rst paper on formal topology [32] was sent to the publisher fteen years ago. It was the
result of two years of intense work, in close collaboration with Per Martin-L of. Since then, I …

The aim of this paper is to relate algebraic quantum mechanics to topos theory, so as to
construct new foundations for quantum logic and quantum spaces. Motivated by Bohr's idea …

Formal topology aims at developing general topology in intuitionistic and predicative
mathematics. Many classical results of general topology have been already brought into the …

Intuitionism is a philosophy of mathematics that was introduced by the Dutch mathematician
LEJ Brouwer (1881–1966). Intuitionism is based on the idea that mathematics is a creation …

The formal systems that are nowadays called λ-calculus and combinatory logic were both
invented in the 1920s, and their aim was to describe the most basic properties of function …

2. We now look at some basic examples of higher-order constructs and their sheaf models.
Firstly we recall a few fundamental facts. Peano's axioms are categorical by the usual proof …