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 …

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

Publisher Summary The λ-calculus represents a class of (partial) functions (λ-definable
functions) on the integers that turns out to be the class of (partial) recursive functions. The …

Both pre-orders and metric spaces have been used at various times as a foundation for the
solution of recursive domain equations in the area of denotational semantics. In both cases …

Publisher Summary The chapter presents correspondence between topoi and theories that
makes precise Lawvere's claim that the notion of topos summarizes in objective categorical …

Quasitopoi generalize topoi, a concept of major importance in the theory of Categoreis, and
its applications to Logic and Computer Science. In recent years, quasitopoi have become …

While categorical logic is of very recent origin, its evolution is inseparable from that of
category theory itself, so rendering it effectively impossible to do the subject full justice within …

This Element is an exposition of second-and higher-order logic and type theory. It begins
with a presentation of the syntax and semantics of classical second-order logic, pointing up …

We describe the formal system of higher—order intuitionistic logic with power types and
(impredicative) comprehension which provides the basis for our" set theory"; this is adapted …

This essay is an attempt to sketch the evolution of type theory from its beginnings early in the
last century to the present day. Central to the development of the type concept has been its …