Toposes and Local Set Theories: An Introduction: 14 (Oxford Logic Guides) - Tapa dura

In recent years category theory has come to play a significant role in the foundations of mathematics. The invention by Lawvere and Tierney of the concept of (elementary) "topos" may be considered one of the most striking developments in this regard. This concept unites, in a simple way, a number of seemingly diverse notions from algebraic geometry, set theory and intuitionistic logic and has led to the forging of new links between classical and constructive mathematics. This book is an introduction to what may be termed the logical approach to topos theory, that is, the presentation of toposes as the models of theories - the so-called "local set theories" - formulated within a typed intuitionistic logic.