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 …

Categories, Types and Structures. Page 1 HAL Id: hal-03316030 https://ens.hal.science/hal-03316030
Submitted on 10 Aug 2021 HAL is a multi-disciplinary open access archive for the deposit and …

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 …

This chapter provides an introduction to the interaction between category theory and
mathematical logic. Category theory describes properties of mathematical structures via their …

We present the topos S of trees as a model of guarded recursion. We study the internal
dependently-typed higher-order logic of S and show that S models two modal operators, on …

Theories of dependent types have been proposed as a foundation of constructive
mathematics and as a framework in which to construct certified programs. In these …

The categorical approach to recursion theory has produced very interesting results in such
areas as the study of higher-type structure [Hyl77b, Sco80a, LS83](the last contains also …

Semantical analysis of higher-order abstract syntax Page 1 Semantical analysis of higher-order
abstract syntax Martin Hofmann * Synopsis: A functor category semantics for higher-order abstract …

Among these logics that deal with the familiar connectives and quantifiers two stand out as
having a solid philosophical-mathematical justification. On the one hand there is a classical …

This paper is concerned with a remarkable fact. The effective topos contains a small
complete subcategory, essentially the familiar category of partial equivalence realtions. This …