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 …

Standard formulations of intuitionistic logic, whether by logicians or by category theorists,
generally do not take into account partially defined elements.(For a recent reference see …

Until the mid-twentieth century, topological studies were focused on the theory of suitable
structures on sets of points. The concept of open set exploited since the twenties offered an …

This book is about some recent work in a subject usually considered part of" logic" and the"
foundations of mathematics", but also having close connec tions with philosophy and …

Publisher Summary This chapter describes the most accessible of the series of toposes that
can be constructed from notions of realizability: it is that based on the original notion of …

There are basically two ways to view intuitionistic logic: as a philosophical‐foundational
issue in mathematics; or as a technical discipline within mathematical logic. Considering first …

Introduction. A celebrated reviewer once described a certain paper (in a phrase which never
actually saw publication in Mathematical Reviews) as being concerned with the study of" …

Topos theory has led to unexpected connections between classical and constructive
mathematics. This text explores Lawvere and Tierney's concept of topos theory, a …

From the point of view of non-classical logics, Heyting's implication is the smallest
implication for which the deduction theorem holds. This book studies properties of logical …

This third edition, now available in paperback, is a follow up to the author's classic Boolean-
Valued Models and Independence Proofs in Set Theory,. It provides an exposition of some …